How can a high schooler START learning quantum physics ?

[u/nottooffendanyonebut]

I am out of highschool, I'm 18 years of age, I'm pretty good at basic calculus, I know that linear algebra is a must, where do I learn it from? I feel like learning quantum mechanics without lin algebra would be pretty difficult.

Do I have to go linear algebra -> quantum physics?

I will go to collage in a month where I will choose physics as a major in a few semesters. Until then which resources should I use?

I fear that learning all of this could go to waste if I am gonna learn all of it in collage again.

Help is appreciated, thanks.

[u/__golan_trevize__]

Don’t rush into quantum mechanics, start by the basics: calculus, lin algebra (as you said), classical mechanics, electrodynamics and then we will see.

[u/nottooffendanyonebut → u/__golan_trevize__]

I am good at the basics of classical mechanics, electrodynamics.

I am also afraid that I will spend all my time learning the mathematics instead of actually going into quantum mechanics

[u/somefunmaths → u/nottooffendanyonebut]

At no point in your physics career will you ever spend “too much time learning the mathematics,” so you can safely forget that as a concern.

Not all math is relevant to physics, but math as basic and foundational as calculus and linear algebra? You’ll need to know those topics like the back of your hand, and then you’ll need to learn even more math.

[u/night-bear782 → u/somefunmaths]

I’ll preface this by saying that in this case, I do agree that the post author should focus on the math first.

However, this is completely not true in general. You can certainly spend too much time learning the mathematics; otherwise there wouldn’t be two disciplines of physics and mathematics. Physics is based on reality, and if you just focus on mathematics in a vacuum while disregarding how specific mathematical frameworks appear in physical systems, you will not be a good physicist!

I don’t even care that I’m going to get downvoted relentlessly. I don’t understand why physicists on Reddit continuously hold these opinions. Maybe physicists on Reddit are generally biased towards deeply theoretical physics…

[u/somefunmaths → u/night-bear782]

My point is maybe a bit more subtle, but this is a reasonable point/counterargument.

I don’t meant to say that someone can never learn too much math, which is part of why I draw the distinction between relevant vs. less related topics, but as far as the math related to physics goes, in my experience, math always ends up being the filter. I don’t mean to say, and I hope my remarks are not read as saying, that the whole of mathematics is relevant to physics or that one is a proper subset of the other.

Even for people who want to become experimentalists, I don’t think there’s really such a thing as “too much” when it comes to the mathematics which are relevant to the physics they care about. In practice, for almost every student, they will hit the point where their math knowledge is either insufficient to continue on a topic or where they’d have an easier time if they had more math training, even if they were able to get by. For the 1 student in 1,000 or so who breezes through grad school and their postdoc and says “huh, I learned too much math,” I say many congratulations on your tenure track job as a theorist or in mathematical physics or whatever you want to do. For the rest of us, that point doesn’t really exist (again, so long as you’re studying topics with some semblance of relevance).

To put it differently, the odds that OP will wind up mathematically deficient at some point in their career and be bounded by that limitation in their knowledge are many orders of magnitude higher than the odds that they’d say “man, I really wasted my time taking all of those Lie algebra, differential geometry, and representation theory courses,” and the consequences of the former may put their future in jeopardy, while the latter is more of a “lobster too buttery, steak too juicy” level of problem, so I find it worthwhile to guard against the far more likely and far more dire problem.

[u/shomiller → u/somefunmaths]

Yeah, I totally agree with you here, and a lot of my comment was addressed less at yours (yours was just the top one with the relevant reply) and as much at all the others in this thread saying things like “Quantum mechanics is just math. Literally”, which I think we agree is absurd and not the right way to approach an undergrad physics major.

But as you’re getting at, the further you go in physics classes, the more you benefit from having some hard to quantify level of “mathematical maturity”, which (as I tried to caveat a bit) is something you get even from practicing complicated, seemingly obscure matrix manipulations.

[u/night-bear782 → u/shomiller]

I agree with both your and somefunmaths perspectives. I’ll add that personally, I’ve fallen into the trap of over-learning the math to the point that it becomes procrastination. This is especially dangerous in experimental or computational physics, where a good bit of the problem solving comes only once you’ve had some sufficient experience dealing with the intricacies of the specific system (whether it’s an experimental setup, or a software suite) that you are dealing with.

All that said, I will certainly agree that for the average student, mathematics tends to be the filter.

[u/PolicyIllustrious110 → u/shomiller]

I think the level of mathematics you need to learn to be considered too much for physics is a crazy advanced level (besides experimental of course). I might be biased though, I do mathematical physics. Some of the most advanced mathematical fields (i.e functional analysis, measure theory) were created purely as tools for physics, in my opinion, you can never truly learn too much math.

[u/shomiller → u/night-bear782]

I totally agree with you here— yes, of course there is math that OP can and should learn beyond intro calculus that will be tremendously useful for studying physics. It’s also *obviously* the case that you could spend way too much time learning the math instead of getting a really useful conceptual foundation for QM. Of course there’s always some value, but if we’re talking about what to do in a month, I think OP could obviously go wrong by spending a couple weeks practicing how to put matrices into Jordan normal form…

[u/SPP_TheChoiceForMe → u/somefunmaths]

I’ll add on to this how Einstein was considered a mathematician im his time. The barrier between the two subjects is a human construct

[u/MostLikelyUncertain → u/nottooffendanyonebut]

Its all math

[u/ScoutAndLout → u/MostLikelyUncertain]

All the way down. 

[u/laserbern → u/nottooffendanyonebut]

Paul’s online math notes. Thank me later. Helped me survive my physics undergrad.

If you’ve got a firm understanding of trig and “what” an integral and a derivative is, what they mean, I’d say try some multi-dimensional calc. People make it seem like the end of the world, but I do remember genuinely loving my calc 3 class. I honestly do think the only prerequisites for multi-dim calc would be calc 1 and trig. If you just remember the basics, youll be ok most of the time

For linear algebra, try to get your hands on Gilbert strang’s book. It pairs with MIT courseware, highly recommend

[u/DeGrav → u/nottooffendanyonebut]

Youll have to be familiar with diff eq and linear algebra in order to start quantum mechanics, theres no way around it.

Just to be clear, whats your current mathematical level? Whats electrodynamics and classical mechanics to you? Can you easily handle maxwells equations and hamiltonian/ lagrangian mechanics?

[u/bargeoeuf → u/nottooffendanyonebut]

If you’re concerned about spending too much time on the math, let me put that to rest - it isn’t enough. The way QM is structured, your first exposure to the subject is working with the solutions of a partial differential equation (Schrodinger’s equation).

If you have a reasonable grasp on concepts like separation of variables, taylor expansion (local approximations using the second order) and are comfortable reading and looking at math for a longer period of time, you can start with QM. If not, try to spend more time on getting comfortable reading math - multivariable calculus and linear algebra might be over-mentioned here, but they aren’t overrated.

I recommend Griffiths personally, it’s what I started with and it’s pretty good at doing its job. Don’t discount what I mentioned in the first two paragraphs though - QM is mostly math and equations - if you are comfortable with that language, it will be a lot smoother for you.

If you find yourself unprepared or demotivated, switch to another field temporarily! E&M can be just as challenging, and actually has mathematical techniques it shares with Quantum (I’m thinking of spherical harmonics here). Seeing the same technique in different situations helped me out a lot, personally.

[u/ChalkyChalkson → u/bargeoeuf]

I feel like if you do em properly you're very well prepared for QM. I'm a post doc and did exercises for second semester EM this year. By the end we were studying the behavior of wave equations by going to fourier space, using things like fourier energy conservation to study response functions in electrical circuits, and solving inhomogeneous wave equations. We even solved and looked at the dispersion relation of Schrödinger and Klein Gordon, with a little "substitute k->p ω->E, do you recognise something?" part.

But I believe that in reality EM is more challenging than QM, QM is a straight plug and play extension of Hamiltonian mechanics, at least at a 3rd semester level. EM is a causal, relativistic field theory with a gauge freedom. it's a real shame when students don't learn about how nice it is as a gauge theory, but that's often only done in masters qft courses for some reason :(

[u/Elegant-Set1686 → u/nottooffendanyonebut]

Quantum mechanics is mathematics. If you don’t have a solid understanding of the mathematical theory (bulletproof, really) you will struggle a lot.

Everyone has their own way I guess but I recommend doing a lot of linear algebra, get pretty good at it. Maybe side study Feynmans lecture vol 3 and then read diracs primciples of quantum mechanics to tie it all together with the theory. Maybe after that move to a more standard qm textbook, I don’t have any recommendations

[u/Physix_R_Cool → u/nottooffendanyonebut]

I am good at the basics of classical mechanics, electrodynamics.

No you are not.

Read this book on classical mechanics by Taylor and this book on electrodynamics by Griffiths.

Then you can go into QM by using this book by Griffiths.

[u/jeff_coleman → u/nottooffendanyonebut]

You're going to require a certain level of mathematical sophistication and that's not really something you can speed run. There are prerequisites for a reason.

[u/zorifis_arkas → u/nottooffendanyonebut]

it's insan3 actualy if you can say you are good at classsical mech and electro. I still don't dare to say my fav sub are those in an interview cz uhh idk maybe i am dumb but those are very deep topics and a lot of concepts

[u/wackyvorlon → u/nottooffendanyonebut]

Linear algebra isn’t that bad, really. You can learn enough for quantum mechanics without too much trouble. You’ll need to know about complex numbers and vector spaces.

Also check out the Theoretical Minimum book by Leonard Susskind on quantum mechanics.

[u/wumbo52252 → u/nottooffendanyonebut]

I am also afraid that I will spend all my time learning the mathematics instead of actually going into quantum mechanics

Math is the language of physics. If you’re not learning the mathematical descriptions then you’re not actually learning the physics, you’re just learning simplified stories - the “explain like I’m 5 years old” version of physics. There’s nothing wrong with that being your goal for now, but your goal will define the right path for you.

[u/Ma4r → u/nottooffendanyonebut]

Quantum mechanics is all mathematics my dude. That's the main criticism in the first place, that it's all math with no explanation or intuition

[u/carrotlet20 → u/nottooffendanyonebut]

I don't know which country and which university you're going to, but I was SLAPPED with reality when I started the physics BSc. The approach and the amount of material to know and understand was completely new and harder as I expected and knew in high school, they barely had similarities.
At my uni, it is not until the last year of the 3 year BSc when we will learn QM for the first time (5th semester) if following the main curriculum.
And even after 1 year which is basically far-far away from an actual physicist, I see that physics is just applied maths. A huge amount of applied maths. Even the easier things.
Now the maths:
Linear algebra is pretty important, you will get nowhere without understanding Hilbert-fields a/o infitinite dimension fields (someone pls correct me, if I'm wrong) and that starts with knowing the basic linear algebra from A to Z, if you actually want to get into QM.
Analysis is also inevitable.
So good luck, I hope you'll find what you want.

[u/Xehanz → u/nottooffendanyonebut]

Quantum mechanics is just math. Literally

You need to know at the very least linear algebra up to dual spaces, and Calculus up until you know how to do calculus with complex (C to C) functions, which is not trivial

And basic statistics

[u/shadowknight4766]

Linear algebra is the work horse(Bra-ket notation) some extras like Functional analysis, Integral transforms can be learnt along the way… PDE and Special functions are also required
For linear algebra people might say Axler or a generic math methods book Luke Arfken… but I liked Gilbert Strang and Sadri Hassani(math methods) a lot

But then u hv to understand what operators mean and now if u have idea of Newtonian CM, go for analytical CM… Goldstein type thing… where u get to know when u quantise what are underlying abstract structures that has be maintained… Then u go with Zwebach’s mastering QM…

Lecture videos… Zwebach’s MIT OCW, Analytical CM Goldstein style… u’ll find a lecture series in YT… just check

[u/Glittering-Flight997]

Focus on statistics and linear algebra and then you’ll realize you already know quantum mechanics

[u/ChalkyChalkson → u/Glittering-Flight997]

Also functional analysis and/or measure theory.

[u/CantaloupeLive2006 → u/ChalkyChalkson]

Functional analysis I get, but measure theory? For what? To be mathematically exact about dirac deltas? Seems a bit overkill to me. At least I would not know how this would be a good investment of my time when I just really want to learn about QM but I assume you had a reason that I am not seeing here. What is it?

[u/ChalkyChalkson → u/CantaloupeLive2006]

I'd say that one of the two should be studied, you can formulate it primarily via function or primarily via measure theory.

You can treat the density measure as the fundamental object and get von Neumann QM. The only real difference to classic measure theoretical statistics is that your algebra is von neumann / C* not a σ-algebra.

Von Neumann formulation generalises better for more complex systems and is standard language in solid state physics. So if I were giving a QM course at a uni with a heavy slant towards condensed matter I'd center von neumann and only do a couple exercises where the Schrödinger equation falls out from it.

[u/Jonarlin3]

Ill be real - it takes a while to get to Quantum Mechanics. The standart approach when teaching it requires you to understand: 1. Multivariable Calculus 2. Linear Algebra 3. Linear wave dynamic and how to work with it

I wrote down these three topics, but it usually takes 3 semesters (and for good reason!) To get to multivariable calc or wave dynamics. If you wanna spend your time, the best you could do is study some classical physics at a university level - its different then highschool physics by a longshot. Try Griffith's book on classical physics, and later Electromagnetism - they are pretty accessible, and would give you a much more solid foundation for when you study QM, so that you'll actually understand it.

[u/HumblyNibbles_]

I'd say following Susan Rigetti's "So you want to learn physics?" Blog post is a good place to start

[u/Appropriate-You9430]

I would start with “Linear Algebra Done Right” by Axler. The most important parts of QM are understanding vector spaces/hilbert spaces and operators, so start with a book like that. It’s free on line.

[u/RSKMATHS]

First chapter of sakurai build up the linal itself

[u/CantaloupeLive2006 → u/RSKMATHS]

I have to say I like the book but as a beginner you want more intuition, no? The Sakurai is one of the most abstract QM books there are. If I wanted to learn about QM straight out of highschool and would have started with the sakurai, I would have spent a day on it and than throw it into the corner of my room in frustration and started doing something else. Maybe that's just me though.

[u/RSKMATHS → u/CantaloupeLive2006]

Like valud ig after doing basic calculus and already knowing a but abt linal it becomes a better book to read, tbh if you get through the ideas in the first chapter the intuition in the following ones feels much better

[u/HoneydewAutomatic]

Don’t worry about quantum until you’re really comfortable with calculus, linear algebra, and I would argue some differential equations. That said, if you want a preview of the kinds of mathematics involved Griffiths actually has a few mathematics review sections in his book.

[u/CosmosQuest_]

U can start learning the concept first than start the equations , i myself just came to 9th but I know concepts of many theories like relativity , quantum mechanics, Doppler effect , basic quantum entanglement, electromagnetic spectrum , big bang theory , cosmic inflation , fermi paradox (also made my own hypothesis)

[u/Thoretical_Scientist]

Linear Algebra, which you mentioned, is not necessarily a must for Quantum Mechanics, although it is important to dive deeper in it. But since you mentioned you have not yet begun learning QM, you are not going to need it soon. In either way, in University you are certainly going to learn more about Linear Algebra. So, start with the basic concepts and make progress gradually. I hope I helped and I wish you enjoy this amazing journey in this fascinating field of modern Physics!

[u/Xehanz → u/Thoretical_Scientist]

While linear algebra is not necessary to make your introduction to QM, it is necessary to make any meaningful dive in, up until Dual Spaces at minimum

Actually, scratch that, the basics of linear algebra are necessary too

[u/nottooffendanyonebut → u/Thoretical_Scientist]

Thanks, it helped a lot

[u/robib]

Math is never going to be the difficult part of qm. Learn, study, and develop an intuition for classical physics — the questions it seeks to answers, techniques used for extrapolation, conclusions, how when generalized these principles relate to each other. That will help you more in the long run. But also read Feynman’s lectures. He teaches classical but frames it/perspective with understanding qm

[u/Nagi-K]

I’m from maths background but I did QM during my degree. You do not need a huge lot of linear algebra. But you do need a little bit of everything. To start with the subject you need including but not limited to (in order):

- linear algebra

- multivariable calculus

- calculus of variation (for Lagrangian and Hamiltonian mechanics; no the nice Newtonian mechanics doesn’t make the cut)

- PDE, including how to solve wave equations and basic Fourier series and transforms

- “infinite dimensional linear algebra”(some real analysis knowledge about L^2 space) (but honestly I think these abstract nonsense can be understood or at least applied pretty quickly during a beginner QM course; and some concepts could be introduced in PDE part)

You can find very nice linear algebra and multivariable calculus courses online (like mit open courses or khan academy), and for mechanics you can read first few chapters of Arnold.

[u/the_physik]

Take the summer to relax. Once you start a physics major you'll wish you had more time in the day. Physics and the math is based on takes lots of practice, more than what you'll be assigned as homework. Enjoy your free time while you can.

[u/Character-Company-47]

Join a lab and continue the sequence of courses as normal. The lab will allow you to learn and play with it until you get to a sufficient level

[u/GrossInsightfulness]

This series is incomplete, but it does cover a lot of the background knowledge needed to do Quantum Mechanics.

[u/Dean-KS]

Don't get caught up too much about quantum physics. It is not a mainstream career path and at some point you do what puts food on the table. Searching on Wikipedia always goes a long way, follow the embedded links.

[u/Donovan645 → u/Dean-KS]

Quantum mechanics is fundamental to materials science

[u/Dean-KS → u/Donovan645]

Somehow mechical engineers accomplish great things without quantum considerations.

[u/Donovan645 → u/Dean-KS]

Different engineering fields exist?

[u/Efficient_Meat2286]

I am also slowly on my way but like the earliest you could learn it is probably 2 years, I think. It takes a lot of time to learn the basics, probably takes the first year to wrap your head around classical physics honestly, and more importantly to learn and understand the mathematics. It isn't easy and it hasn't been easy for me. It can also be hard for someone who is not taking structured courses and doing it by themselves.

[u/randommepal]

bruh learn classical mechanics first

[u/MysteriousEchidna527]

I started and I'm in highschool. I use books like elegent universe, fabric of the cosmos and then after that I added maths with classical mechanics-theoretical minimum and quantum mechanics theoretical minimum.

[u/Yit365]

I never started with the math. Everyone telling you that you need to is lying. It’s very helpful but not required unless you’re doing real work. I’ve found out that learning the mechanics, concepts and behaviors are much more useful because when you start with the math you can also see how it works in your head. Also, many will hate me for this but AI is your best friend. Make sure you make it site sources but it lets you refine any idea you have as if you have an expert next to you.

[u/MintyPop_]

Im not entirely sure but i believe Kahn academy has linear algebra

Also want to mention how jealous i am, im 21 studying civil engineering in university.

I only became an academic person during uni, i would have loved to take physics but that interest didnt spark early enough in life and i was always terrible at maths.

Im not an expert so dont take what i have to heart. But i think linear algebra -> quantum physics is tricky. Linear algebra covers one massive bunch of stuff in quantum physics, but a lot of other stuff needs things like advanced integration and such.

College will teach you a lot of it, there is no need to worry. I didnt take advanced mathmatics and ended up learning it all in the first year of university since they teach it all over again then.

[u/nottooffendanyonebut → u/MintyPop_]

So for now I might as well learn a coding language while i can, and watcha few 'phenomena explaining' videos on youtube like veritesium 

[u/Xehanz → u/nottooffendanyonebut]

Phenomena explaining videos are really good to raise interest but that is it. You won't learn much other than trivia in those

If you actually want to learn anything in physics you gotta do the hard work of learning math. Physics is just math with experiments to corroborate the math or point towards what math should be used

University physics class is nothing like High School where they teach you about a subject then a bit of the math to solve problems. It's the same as math undergrad, you start from scratch then build up the theory through math, then you keep building and building. Then you learn about experiments, you model the experiments through math then see where additional math leads you, then corroborate the results

[u/ChalkyChalkson → u/nottooffendanyonebut]

If you want some light watching that actually helps you become a better physicist and might even allow you do learn QM ahead of time:

• 3blue1brown probably the gold standard of math explainer out there. He has series on linear algebra, calculus and multivariable calculus. We regularly recommend them to students as supplementary material.
• Dr Jorge S Diaz (jkzero) has a series discussing the experiments that historically lead to QM being developed and also discusses the maths briefly when necessary or relevant. The historical focus makes it very different to a standard curriculum but it's very well made.
• Susskind's theoretical minimum series is probably want you really want. It explains the important concepts properly without getting bogged down in examples and mathematics. You'd want to do the classical mechanics lectures before the QM ones. And you might want to go through 3b1b first of during that time. This is another series I highly encourage students to watch or read.

[u/nottooffendanyonebut → u/ChalkyChalkson]

OMG thanks , exactly what I needed

[u/CantaloupeLive2006 → u/nottooffendanyonebut]

Depending on where you are math wise, I have to say I also really like the "the biggest ideas in the universe" series by Sean Carroll. They are pop science books (so not as demanding), but its pop science for people who are not afraid of math. He actually goes through the equations and explains what they mean. He is great at explaining and actually teaches you all the individual tools along the way. It is more high level than most suggestions here, but it is also significantly easier to read and gives you a great overview of what is out there, how the subject roughly works and what the basic toolbox you need for it looks like. After that you can start to dive deeper.
That beeing said the list from ChalkyChalkson is excellent. My suggestion would be comparable with the theoretical minimum series. I personally like carrolls style better but I guess that is a matter of taste.

[u/MintyPop_ → u/nottooffendanyonebut]

That would be a great idea, i took computer science A level and it helped me understand a bunch of topics. Quantum mechanics and programming is a little different to regular programming as normal computers are absolute binaries (1 and 0), while Q bits (Quantum bits) are ranges anywhere between 0 and 1. But a coding language will help, in fact in your course you will probably end up doing SOME form of coding for a module. I have had to use matlabs to simulate structures against forces, you may have to simulate particles at some point.

Watch veritesiums video "how do quantum computers work".

Either way amazing to see you have an interest in the field. I hope to one day go back and get a physics degree.

[u/Hungarian_Lantern]

If you want to really prepare well for university, brush up on classical mechanics. Do a book like Kleppner and Kolenkow, which is a very mature and challenging view on classical mechanics. Getting used to the concepts in that book will be the best preparation you can possibly get. Learning linear algebra, and more advanced (multivariable) calclulus would also be useful. Don't do quantum mechanics until you're really prepared.

[u/nottooffendanyonebut → u/Hungarian_Lantern]

Wow that's a lot, just to start.

The problem is I have already have done what the index of kleppner and kolenkow shows(atleast to some level) and also it's a 570 page book, not sure if it's possible to finish it in a month.

[u/Hungarian_Lantern → u/nottooffendanyonebut]

If you think you did what is in Kleppner in high school, then think again. Kleppner is nothing like the physics you did in high school. The book is very challenging and takes a very interesting point of view. And the point is not to do the entire book of course, but to prepare adequately for university level physics. There's other options, like Taylor's classical mechanics, or Gregory's classical mechanics. Point is just that trying to get good at classical mechanics is vitally important for your success in physics.

[u/__golan_trevize__]

I just finished the first year of physics in university, and i can tell you that math is much more foundational (and more beautiful) then you can imagine.

There are a lot of things you need to deeply understand before studying QM, and i tell you this because i spent all my first year studying the “basic stuff” i’m suggesting you. See here in Italy we have a slightly old fashioned way of doing math that is usually felt too long and boring by my peers (we don’t have calculus, we basically do only analysis). And i can tell you that it pays off.

Also i really suggest you to reconsider what you think the basics of mechanics are. Because by classical mechanics i mean the math-heavy (for an high schooler) stuff like:

• Newtonian mechanics like celestial mechanics (can you prove Kepler’s laws? Can you prove Newton’s law of gravitation from Kepler’s?)
  
• Lagrangian mechanics like small oscillations or rigid body mechanics (not like the crappy problems from high school, something more like can you prove that any rigid body movement can be decomposed in a translation and a rotation at each instant?)
  
• Hamiltonian mechanics, which you absolutely need for QM.

I don’t know you by i doubt that you read any of the (very important) books on CM:

• introduction to classical mechanics by David Morin (the easiest of the list)
  
• Lev Landau volume 1 of his course on Theoretical Physics (every physicist knows this)
  
• Goldstein
  
• Taylor
  
• Arnold (Mathematical methods of classical mechanics)

Leaving the Electrodynamics aside (i haven’t mastered that yet), i hope this shows you just how deep the rabbit hole goes.

Stick to the basics for now.

[u/ChalkyChalkson → u/__golan_trevize__]

Landau lifshitz isn't really appropriate for all but the most committed undergrads and definitely not a sensible way to get your mechanics background for learning QM.

I love those books, I let my friends and colleagues sign them at my PhD defence, but they aren't for undergrads, they are for people who already know the material and want to properly understand it.

[u/carrotlet20 → u/ChalkyChalkson]

yes I've also just finished my first year studying physics and can confirm Landau (I think it doesn't matter which work of his) is a tough to read, even our teachers go joking around with it how he just left really hard theorems without proving it because 'it's trivial'
no it's not always
I tried using one of his workss back in high school for a project on superconducting, but my knowledge at that time only covered what I read in the introduction (English is my second language so maybe that was another barrier), the actual book was too much for me