What physics background needed for quantum mechanics?

[Flumpster]

A while back I read that, roughly speaking, these are the main topics that make up the backbone of a physicist's education: classical mechanics, electromagnetism, statistical mechanics/thermodynamics, special relativity, quantum mechanics, and general relativity.

(If that's incorrect, please tell me. I know there's a lot more to physics, I'm just ignoring specialist fields for now.)

If I wanted to learn quantum mechanics, and was less interested in other topics on this list (I like physics, but I'm much more enthusiastic about chemistry, and quantum mechanics appeals to me a lot because of it's relationship to chemistry) would I have to learn all of these topics? If I don't need to learn all of them, which ones do I need? I mean, I assume GR isn't necessary, don't know if the electromagnetism is important or irrelevant..) I'd really appreciate help on this, because right now I'm just guessing.

Thanks! :)

 

[Jorriss]

Outside of Math prerequisites, a foundation in classical mechanics is good for quantum mechanics. The amount of background is debatable but at the very least an intro course and even better is knowing some Hamiltonian CM. Spectroscopy is vital to chemistry and that takes a lot more classical mechanics. If you could, taking a semester or two of upper division classical mechanics is a great idea. That being said... Statistical Mechanics and Thermodynamics are huge in chemistry. If you're excited about chemistry, then you should be excited about those too.

E&M is not as vital but a foundation in that is necessary too.

You can safely skip GR. I honestly do not know if GR has been applied to chemistry ever, in any context.

 

[Clever-Name]

General relativity is definitely NOT a topic that makes up the backbone of physics education. Most physicists won't even study GR at all in their career. The rest looks fine though.

For chemistry your most important courses will likely be QM and Statistical Mechanics/Thermodynamics. EM probably isn't necessary but it's good to have some knowledge of it. CM probably won't be useful to you but I would still recommend taking it, as CM and EM are typically taken before QM.

 

[Flumpster]

Jorriss - Thanks. I was worried that you have to do many classical mechanics courses in order to learn quantum mechanics - an intro course and an advanced course doesn't sound as bad as I thought.

That being said... Statistical Mechanics and Thermodynamics are huge in chemistry. If you're excited about chemistry, then you should be excited about those too.

Oh, I actually am looking forward to Thermodynamics/Stat. Mechanics :) When I said I was less interested in topics other than quantum, I didn't mean all of them.

Mostly, I was referring to SR and GR.

E&M: When you say "not as vital" - is classical E&M something that will be necessary in order to/relevant to understanding quantum mechanics, or is it just part of the physics foundation I should generally have?


Clever-Name - My bad on the general relativity, thanks for correcting me :)

You say that classical mechanics probably won't be useful - why do you say that? (I'm not disagreeing, I just want to know what you think detracts from its value). On one hand I expected classical mechanics to be less useful, on the other hand I see the value in learning the classical concepts before quantum mechanics.
Do you think one course in classical mechanics would be enough, if the end goal is understanding quantum mechanics?

 

[Nabeshin]

E&M: When you say "not as vital" - is classical E&M something that will be necessary in order to/relevant to understanding quantum mechanics, or is it just part of the physics foundation I should generally have?

QM in itself is completely independent of classical electromagnetism. The only real time it becomes useful is applications of QM to classical electromagnetic systems (i.e. some things are quantized, but not the electromagnetic field). The classical example is the hydrogen atom, but all you need to know is the form of the coulomb potential to solve this. Other examples include the corrections to the hydrogen atom because of dipole moments and whatnot, but again the amount of strictly E&M needed to understand this is quite shallow.

 

[chill_factor]

General physics level of EM is good enough, but you have to actually know it at a general physics level (as opposed to not knowing any at all). also should get a good knowledge of optics. if you are doing NMR work maybe a stronger EM knowledge would be useful.

Strong knowledge of classical mechanics is good since you have to know this stuff for spectroscopy or computation; many spectroscopic techniques especially rotational and vibrational need knowledge of *classical* mechanics to calculate moment of inertia, normal modes, etc. Also, molecular dynamics simulations for really complicated systems like proteins, polymers, monolayers, etc. are written with classical interactions only. Taking into account quantum interactions for a gigantic 1000+ atom molecule with another giant 1000+ atom molecule or thousands of solvent molecules each with a few atoms is quite difficult computationally.

As much *nonrelativistic* QM and thermodynamics as possible... this is a no brainer... physical chemistry is all about nonrelativistic QM and thermodynamics, every other chemistry uses physical chemistry.

 

[Vampyr]

If you are just interested in learning quantum, then you only need to have a good grasp of classical mechanics. In fact, many physical chemistry courses will start off with quantum mechanics as the main topic of study. If you are interested in quantum chemistry, you should check out Molecular Quantum Mechanics by Atkins - its quite rigorous but also fairly easy to follow.

For the rest of physical chemistry you will also do a lot of stat mech and thermodynamics. Electromagnetism is usually glossed over by most undergraduate chemistry courses which is a shame because it can be quite useful.

 

[Jorriss]

QM in itself is completely independent of classical electromagnetism. The only real time it becomes useful is applications of QM to classical electromagnetic systems (i.e. some things are quantized, but not the electromagnetic field). The classical example is the hydrogen atom, but all you need to know is the form of the coulomb potential to solve this. Other examples include the corrections to the hydrogen atom because of dipole moments and whatnot, but again the amount of strictly E&M needed to understand this is quite shallow.

This is the sense I meant E&M is not vital, flumpster. You don't need E&M to understand quantum mechanics, but for some applications, you need some e&m.

Again though, more and more e&m shows up as you get deeper into chemistry. It's just natural in chemistry to deal with systems interacting with electric and magnetic fields and this takes some e&m knowledge. If you do theoretical chemistry though, you will need to know the potential formulation of e&m eventually. There are also interesting purely quantum mechanical phenomena that involve e&m, such as the aharonov-bohm effect.

It's worth learning more and more e&m. You don't need the detailed a physicists would know of course.

 

[Clever-Name]

Clever-Name - My bad on the general relativity, thanks for correcting me :)

You say that classical mechanics probably won't be useful - why do you say that? (I'm not disagreeing, I just want to know what you think detracts from its value). On one hand I expected classical mechanics to be less useful, on the other hand I see the value in learning the classical concepts before quantum mechanics.
Do you think one course in classical mechanics would be enough, if the end goal is understanding quantum mechanics?

It's not that CM won't be useful per-se, I guess I could have rephrased myself. I think ultimately the courses you will see a direct use for will be QM and Stat mech/Thermo. I can't think of any situation where you might have to directly use something you learned in CM while working in the chemistry field. However CM is a very interesting subject and having knowledge in it will be beneficial overall. CM is typically learned before QM because towards the end of a class on Langrangian/Hamiltonian dynamics you will deal with topics that tie in quite nicely with topcs in quantum theory like Hamilton's equations, Noether's Theorem, Poisson Brackets, Commutator algebra, etc.

One course in CM would be sufficient. If an advanced course were offered I would recommend taking it though as I'm sure some of the more advanced topics would help in your understanding of QM. Also an advanced course in CM would be extremely interesting. My University has it on the course listings but unfortunately hasn't offered it in a few years. The topics covered are: Hamilton's equations, canonical transformations, symplectic space, Poisson brackets, integrability, Liouville's theorem, Hamilton-Jacobi theory, chaos, classical field theory. All of which I'm sure you can find parallels in QM.

 

[Jorriss]

Classical mechanics shows up in chemistry a lot, in the context of quantum mechanics and statistical mechanics.

One, to formulate classical statistical mechanics requires Hamiltonian mechanics. Granted, we don't need to know all the transformation properties one learns in physics.

Spectroscopy, just intro spectroscopy, requires a knowledge of rotational dynamics beyond what is learned in an intro course (moment of inertia tensor, normal mode analysis, etc). In spectroscopy one will also encounter systems of coupled oscillators, so one will want to know Lagrangian dynamics. There are many more applications.

There is not enough to justify taking a graduate course, unless interested, but there is far more needed than an intro course.

 

[Flumpster]

I understand now. Thank you all for your awesome replies! You've really helped me a lot :)