Best next step for tackling quantum mechanics?

[Agrasin]

I'm a high school student who has completed classical mechanics and electrodynamics with calculus (equiv. AP Physics C).

I'm interested in learning quantum mechanics as soon as I can. I've heard of kids my age who are learning that stuff already. Then I open a textbook and see crazy stuff like Legendre polynomials, Dirac delta function, tensors, etc.

Should I put quantum mechanics aside for now and just learn math? Should I learn MV Calc, linear algebra, and differential equations before tackling quantum mechanics and beyond?

I've come to appreciate so much of modern physics but it has always bugged me how far I am from understanding things like Einstein's field equations and Schrodinger's wave equation. For instance, I tried reading a paper recently and I couldn't even fully understand how the Minkowski metric works.

 

[jbrussell93]

I never took AP physics so I'm not completely sure what you have actually covered in CM and E+M but you may want to spend some time developing a deeper understanding of those, as well as mathematical prerequisites first. For example, have you been exposed to Lagrangian and Hamiltonian formulations in classical mech? What about boundary value problems in electromagnetism? In order to really understand these things, you will need vector calculus and differential equations. I would suggest not trying to rush into quantum mechanics without having the proper foundations.

 

[jbrussell93]

I would suggest an intro modern physics text such as Modern Physics by Raymond A. Serway. This is the book I used in my second year modern physics course. It's pretty mathematically lite and is a great introduction to the ideas of modern physics and some of the historical context. There is an elementary treatment of quantum mechanics beginning about half way through the book.

 

[jtbell]

I second the suggestion above. There are several other similar texts: Ohanian, Taylor/Zafiratos/Dubson, etc. These books also introduce you to relativity and some application areas like atomic, molecular, nuclear, solid state and particle physics.

 

[Agrasin]

Okay, well now I'm doubting whether rushing into modern physics is a good idea.

If I'm interested in a career in pure physics, should I spend more time right now reinforcing my foundation? I don't know what the Lagrangian and Hamiltonian formulations of classical mechanics are. I wikipedia'd them and they appear to require some MV calc. So should I pursue advanced classical mechanics and electrodynamics (although I don't like electrodynamics much)?

AP Physics C Mechanics and Electricity+Magnetism are courses that reintroduce the basic equations (f=ma, V= IR) in calculus form (f = dp/dt, V = dq/dt R). They test simple derivatives and simpler integrations (for instance line integrals using Ampere's Law).

 

[WannabeNewton]

If I'm interested in a career in pure physics, should I spend more time right now reinforcing my foundation?

Yes without a doubt.

(although I don't like electrodynamics much)?

Well that's a first for someone interested in pure physics. I can only think of one thing I would find more satisfying and exciting than EM.

AP Physics C Mechanics and Electricity+Magnetism are courses that reintroduce the basic equations (f=ma, V= IR) in calculus form (f = dp/dt, V = dq/dt R). They test simple derivatives and simpler integrations (for instance line integrals using Ampere's Law).

If AP Physics C still has the same basic curriculum it did ~2 years ago then you need a lot more physics before jumping into QM if you want to study QM at a satisfying level of formalism.

 

[Agrasin]

Well that's a first for someone interested in pure physics. I can only think of one thing I would find more satisfying and exciting than EM.

Can't tell if that's sarcastic haha.

If AP Physics C still has the same basic curriculum it did ~2 years ago then you need a lot more physics before jumping into QM if you want to study QM at a satisfying level of formalism.

The curriculum hasn't changed. I think it's pretty shallow-- no respectable university should place students based on scores from this exam.

Also, it sounds like you took AP Physics C two years ago? Do you have any suggestions for me, especially regarding my next textbook? Should I go through a MV Calc textbook, a college-level mechanics textbook, o something else?

 

[ZapperZ]

What exactly is a "career in pure physics"? What subject areas does someone in pure physics do? What areas are not pure physics? If you look at all the different areas of physics as listed in the APS, which ones are pure physics, and which one are the "impure" physics?

Zz.

 

[Agrasin]

@ZapperZ I said that to mean not applied physics, i.e. not engineering. Not sure what the APS is.

 

[ZapperZ]

At Stanford, for example, applied physics includes condensed matter physics, atomic/molecular physics, etc., i.e. Not engineering. Are you ruling those out as well?

APS= American Physical Society.

Zz.

 

[Agrasin]

To be completely, immaturely honest, *points at Einstein* I want to do what he's doing.

Modern physics. The stuff you see on Fabric of the Cosmos and shows like that. Maybe when I choose to specialize in a specific field, I'll have to learn some condensed matter physics or something, but for now I want to develop the foundation for modern physics. (I hope I'm still not too vague).

 

[ZapperZ]

The photoelectric effect is really a condensed matter physics topic.

Last time I checked, Einstein got the Nobel prize for that!

And just to blow this out even more, the Higgs mechanism that is ubiquitously part of elementary particle physics, came out of condensed matter.

You have a lot to learn, grasshopper.

Zz.

 

[ZombieFeynman]

The photoelectric effect is really a condensed matter physics topic.

Last time I checked, Einstein got the Nobel prize for that!

And just to blow this out even more, the Higgs mechanism that is ubiquitously part of elementary particle physics, came out of condensed matter.

You have a lot to learn, grasshopper.

Zz.

Why are you calling the Anderson mechanism the Higgs mechanism anyway? :tongue:

 

[ZapperZ]

Why are you calling the Anderson mechanism the Higgs mechanism anyway? :tongue:

I didn't. I said it came out of condensed matter. I didn't say they are identical.

Zz.

 

[ZombieFeynman]

I didn't. I said it came out of condensed matter. I didn't say they are identical.

Zz.

All of the CMT faculty at my current institution will call the Anderson-Higgs mechanism what the HEP facult call the Higgs mechanism. I've heard arguments break out in colloquia between one of the founders of SUSY and a famous CMT faculty member about whether priority should go to Nambu or Goldstone. P**sing contests everywhere. :rofl:

 

[verty]

Okay, well now I'm doubting whether rushing into modern physics is a good idea.

If I'm interested in a career in pure physics, should I spend more time right now reinforcing my foundation? I don't know what the Lagrangian and Hamiltonian formulations of classical mechanics are. I wikipedia'd them and they appear to require some MV calc. So should I pursue advanced classical mechanics and electrodynamics (although I don't like electrodynamics much)?

AP Physics C Mechanics and Electricity+Magnetism are courses that reintroduce the basic equations (f=ma, V= IR) in calculus form (f = dp/dt, V = dq/dt R). They test simple derivatives and simpler integrations (for instance line integrals using Ampere's Law).

I wouldn't shy away from reading advanced books, even if you don't understand them you will still pick some things up. I compare it to traveling, if you were someone who liked to travel, would you study map books or would you just go and figure it out when you get there? I mean, that's part of the fun. I anticipate that people may disagree with this but who is so rigid that they can spend years learning difficult math without getting bored or disinterested? One needs to vary it a little.

PS. Though I do emphasize, the foundational learning must be done very thoroughly, just intersperse it with some exploration for a little variety.

 

[Fusiontron]

Learn linear algebra. Learn Dirac notation.

 

[WannabeNewton]

Can't tell if that's sarcastic haha.

No that's not sarcasm. If you don't like EM then I can't imagine you enjoying more advanced physics. That being said, EM isn't done any justice in AP Physics C so you might still enjoy it once you see it done properly in a Griffiths based class.

Should I go through a MV Calc textbook, a college-level mechanics textbook, o something else?

You should try to tackle a college-level mechanics book like Kleppner and Kolenkow. MV Calc is very easy to learn so go ahead and learn that in conjunction if you have time.

 

[Fusiontron]

Griffiths is horrid for both QM and E&M. Get Shankar for QM and the Dover reprint of Schwartz for E&M.

 

[ZombieFeynman]

Griffiths is horrid for both QM and E&M. Get Shankar for QM and the Dover reprint of Schwartz for E&M.

I disagree. Although Schwarz and Shankar are fine books, Griffiths has its place as well.

 

[megatyler30]

I have a similar question, which quantum mechanics book should I be able to handle? I'm in 11th. I know multivariable calculus and differential equations although I won't be learning Linear Algebra until the second half of summer and I don't want to wait that long to start QM. So any suggestions?

 

[ateixeira]

Take a look at this blog. The author is doing a study of Griffiths' book on Quantum Mechanics: http://physicsfromthebottomup.blogspot.com/2009/02/the-quantum-gang.html

You'll see a lot of explanations and solved exercises and I think that with your background you are able to understand what's going on.

 

[TheAustrian]

Electromagnetism is a horrible subject in school-level, because nothing is explained, no foundations are given, just some formulae are given "as is". However, EM and Optics becomes much more beautiful, once it is properly introduced.

 

[Agrasin]

By optics I hope you mean an in depth study of light, deriving the wave equation from Maxwell's equations, etc. Not the mirrors and lenses crap that we have to suffer in high school.

 

[Jorriss]

Griffiths is horrid for both QM and E&M. Get Shankar for QM and the Dover reprint of Schwartz for E&M.

Griffiths QM is arguably not great but Griffiths E&M is superb pedagogically.

Griffiths QM is alright but there are much better texts at a similar level. Zettili > all.

 

[TheAustrian]

By optics I hope you mean an in depth study of light, deriving the wave equation from Maxwell's equations, etc. Not the mirrors and lenses crap that we have to suffer in high school.

Yes, Optics and EM become unified into one theory later on. You'll learn about the 4 Maxwell Equations, and later you will solve them to give you the wave-equation, etc.
I'm happy to give you some guidance on this if you want.