Physics Prereqs for Sakurai's Modern Quantum Mechanics

[doggydan42]

Hello,

I've seen some ask about math prereqs for Sakurai's Modern Quantum Mechanics, but I was wondering about the physics prereqs as well. Should classical mechanics and electrodynamics be studied beyond first-year physics courses? Also, is statistical physics needed?

What are the physics prereq's for Sakuria's Modern QM?

Thank you in advance.

 

[Wrichik Basu]

I have mostly seen Sakurai's book being recommended as an advanced text. Many institutions and professors recommend it after Griffiths. From the contents of Sakurai's book, I feel you should at least complete the first three chapters of Griffiths before starting Sakurai. The third chapter in Griffith's book, Formalism, has some of the basic maths required for QM. With these, you should be more or less ready.

Keep Griffiths handy, because you might need to fall back one something if you don't understand what Sakurai is writing.

 

[doggydan42]

I have mostly seen Sakurai's book being recommended as an advanced text. Many institutions and professors recommend it after Griffiths. From the contents of Sakurai's book, I feel you should at least complete the first three chapters of Griffiths before starting Sakurai. The third chapter in Griffith's book, Formalism, has some of the basic maths required for QM. With these, you should be more or less ready.

Keep Griffiths handy, because you might need to fall back one something if you don't understand what Sakurai is writing.

Thank you for the advice. I've completed the 8.04x, 8.05x, and 8.06x QM series on edX, so that was my motivation to move on to Sakurai's. But I have never taken an advanced/intermediate classical dynamics and electrodynamics course. I have also never taken statistical physics. I understand that as part of the physics core, it would good to learn these before advancing, so I was wondering if Sakurai required knowledge in those fields, or if I should still be able to understand the book without them.

 

[Wrichik Basu]

Thank you for the advice. I've completed the 8.04x, 8.05x, and 8.06x QM series on edX, so that was my motivation to move on to Sakurai's. But I have never taken an advanced/intermediate classical dynamics and electrodynamics course. I have also never taken statistical physics. I understand that as part of the physics core, it would good to learn these before advancing, so I was wondering if Sakurai required knowledge in those fields, or if I should still be able to understand the book without them.

Classical dynamics is not strictly necessary for understanding QM at this level. You would work with the Lagrangian and Hamiltonian formalism when you start QFT (specifically, the S-matrix, Feynman's rules, etc.). But here you would need to know what the Hamiltonian is. If you have done these in edX, you can proceed to Sakurai.

Electrodynamics might be necessary at a preliminary level. It will be good if you know Maxwell's equations, and how to write the E and B fields in terms of the scalar and the vector potentials. It might also help to know something about gauge transformations, but these are not absolutely necessary.

You don't need statistical physics for Sakurai (or Griffiths).

Let me share an advice that a professor I know told me once. He said that it is not always possible to keep on doing maths and pause physics completely, because any physicist would be bored. He said that if you get stuck at some topic, pause your current reading, read up that topic from another book, and continue with whatever you were reading. Although he said this for maths related to physics, you can easily extend this to your case as well. For example, if you get stuck with electrodynamics, stop and read it up from some book or lecture, and then return to what you were reading.

Unless you actually start with the book, you will not be able to understand what you really need. It is like fidgeting with the steering wheel but not letting your car move - you will not be able to understand how much you have to steer unless you actually let the car move slowly.

I found these lectures very useful when I was studying at your level:

Quantum Physics by Prof. V. Balakrishnan (NPTEL)
Classical Physics by Prof. V. Balakrishnan

In the second link, you will find some lectures where he talks about classical electrodynamics. You can study from those before or while doing Sakurai. In fact, these lectures are gold mines. I recommend Prof. Balakrishnan's lectures to anyone who is interested in physics.

 

[doggydan42]

Classical dynamics is not strictly necessary for understanding QM at this level. You would work with the Lagrangian and Hamiltonian formalism when you start QFT (specifically, the S-matrix, Feynman's rules, etc.). But here you would need to know what the Hamiltonian is. If you have done these in edX, you can proceed to Sakurai.

Electrodynamics might be necessary at a preliminary level. It will be good if you know Maxwell's equations, and how to write the E and B fields in terms of the scalar and the vector potentials. It might also help to know something about gauge transformations, but these are not absolutely necessary.

You don't need statistical physics for Sakurai (or Griffiths).

Let me share an advice that a professor I know told me once. He said that it is not always possible to keep on doing maths and pause physics completely, because any physicist would be bored. He said that if you get stuck at some topic, pause your current reading, read up that topic from another book, and continue with whatever you were reading. Although he said this for maths related to physics, you can easily extend this to your case as well. For example, if you get stuck with electrodynamics, stop and read it up from some book or lecture, and then return to what you were reading.

Unless you actually start with the book, you will not be able to understand what you really need. It is like fidgeting with the steering wheel but not letting your car move - you will not be able to understand how much you have to steer unless you actually let the car move slowly.

I found these lectures very useful when I was studying at your level:

Quantum Physics by Prof. V. Balakrishnan (NPTEL)
Classical Physics by Prof. V. Balakrishnan

In the second link, you will find some lectures where he talks about classical electrodynamics. You can study from those before or while doing Sakurai. In fact, these lectures are gold mines. I recommend Prof. Balakrishnan's lectures to anyone who is interested in physics.

Thank you for recommending those lectures, I will definitely check them out, and for your advice on reading a textbook and getting stuck.

I have a question a bit off topic from what I asked. I asked about the physics needed, but I am slightly curious if two subjects in math are needed. Do you think I should study tensors and group theory, with maybe https://www.amazon.com/dp/3319147935/?tag=pfamazon01-20, before reading sakurai's, or would it be helpful but not necesary?

 

[Wrichik Basu]

I have a question a bit off topic from what I asked. I asked about the physics needed, but I am slightly curious if two subjects in math are needed. Do you think I should study tensors and group theory, with maybe https://www.amazon.com/dp/3319147935/?tag=pfamazon01-20, before reading sakurai's, or would it be helpful but not necesary?

If I remember correctly, you won't require tensors until you start relativistic QM (and thereafter QFT). Group theory would be required to some small extent when you do angular momenta. Actually the angular momenta generate rotations in SO(3), and there is a very elegant correspondence between SO(3) and SU(2). But most books don't mention this, so you can go ahead without group theory. I learned this for the first time in Prof. Balakrishnan's QM lectures (specifically lecture 24, time 35:45 (from my handwritten notes where I have noted the time for future reference)). A somewhat more detailed discussion is in his Classical physics series (from lecture 32).

You may also like to study the whole of angular momenta from his lectures (from #17, time 25:30), but if you are satisfied with Sakurai, you are welcome to skip them if you wish. You can aptly say that I learned basic QM from Balakrishnan (in conjunction with Griffiths).

In his classical physics lectures, Prof. Balakrishnan has discussed the tensor notation in a good detail. Check them out too (the lectures on Special Relativity).

With these, you should be ready for Sakurai (or perhaps "over-ready"). You can start Sakurai first, and on the way, go through these lectures.

 

[andresB]

Sakurai do have a section on tensor operator, a very badly written section If I remember it correctly. I would not recommend Sakurai after Griffiths, not because it is too advanced, but because it is an unpolished book. Some sections are a masterpiece, others are unreadable.

There are plenty of other books at an intermediate level that I'd recommend first, like Cohen-Tannoudji or Shankar.

 

[vanhees71]

Hello,

I've seen some ask about math prereqs for Sakurai's Modern Quantum Mechanics, but I was wondering about the physics prereqs as well. Should classical mechanics and electrodynamics be studied beyond first-year physics courses? Also, is statistical physics needed?

What are the physics prereq's for Sakuria's Modern QM?

Thank you in advance.

I think to start with non-relativistic QM from the physics side classical mechanics (including analytical mechanics, particularly Hamilton mechanics and Poisson brackets; some Lie-group theory within this formalism doesn't hurt either, but that's not mandatory) and (even more important) classical electrodynamics (not necessarily in relativistic covariant form, if you are not aiming right away to relativistic QFT) are indispensable prerequisites.

I'd not like to teach statistical physics before quantum theory, and that's usually not done in German theoretical-physics courses (I mean the main theoretical physics lectures which usually are taught in the order classical mechanics (including math for physicists), analytical mechanics (Lagrange, Hamilton), classical electrodynamics, non-relativistic QM, statistical physics). The reason is that classical statistics is more complicated than quantum statistics in some way, and you cannot avoid serious trouble without using quantum concepts (particularly the indistinguishability of identical particles). From the very beginning you need quantum concepts, if you don't want to hit the difficulties that plagued Boltzmann, who got it right because of his ingenious physics intuition. I think, it's safe to say nowadays that classical microscopic theories of matter are all flawed, and the classical behavior of macroscopic matter is an emergent phenomenon which can be derived via quantum statistical methods.

 

[Wrichik Basu]

I'd not like to teach statistical physics before quantum theory, and that's usually not done in German theoretical-physics courses (I mean the main theoretical physics lectures which usually are taught in the order classical mechanics (including math for physicists), analytical mechanics (Lagrange, Hamilton), classical electrodynamics, non-relativistic QM, statistical physics). The reason is that classical statistics is more complicated than quantum statistics in some way, and you cannot avoid serious trouble without using quantum concepts (particularly the indistinguishability of identical particles). From the very beginning you need quantum concepts, if you don't want to hit the difficulties that plagued Boltzmann, who got it right because of his ingenious physics intuition. I think, it's safe to say nowadays that classical microscopic theories of matter are all flawed, and the classical behavior of macroscopic matter is an emergent phenomenon which can be derived via quantum statistical methods.

I second that. In fact, I started off with QM soon after finishing Hamiltonian dynamics, but realized later that much of it is not required in the basic courses. My motivation for studying QM was to escape the complex phase portraits of classical physics. Later on, however, when I returned to classical stats, I realized that it was a bit too much than what I could take. You actually don't require all these stuff for studying QM. Lagrangian and Hamiltonian dynamics, Maxwell's electrodynamics and relativity should be enough, or may be more than enough for starting at Griffiths' level.

 

[vanhees71]

I'd only not recommend Griffiths, because it's too sloppy and thus causes often confusions (at least regularly in the forum). I'm not sure what to recommend, if you don't want Sakurai as the introductory textbook. It was my introductory textbook in the QM lecture, and I liked it very much. If you are after a more conventional "wave-mechanics first" treatment, maybe the Feynman Lectures vol. III, Messiah, or Landau-Lifshitz vol. 3 are good choices. I've also heard Cohen-Tanoudji is good, though I don't know this (I think 2 volume) textbook very well.

 

[Wrichik Basu]

If you prefer neither Griffiths nor Sakurai, check out Ramamurti Shankar's Principles of Quantum Mechanics.