Help on Learning Quantum Mechanics (Undergraduate)

[magiladd]

Summary:: I am in the highest level Quantum class at my university- technically considered a grad class. I am an undergrad and need advice on just how to learn it. What study tips? Good Youtubers? Physical simulations? Anything that helped you in quantum mechanics.

Hello! I am an undergrad taking the highest level quantum mechanics class at my university. I am a physics major and I try very hard but I still do poorly in comparison to everyone else. And I love physics too much to do anything else.

I want to know what resources helped you in college quantum classes. I learn visually a lot better than verbally and would love any advice on videos/YouTubers/websites/simulations that help to visualize what is happening.

For instance, I know what eigenstates, eigenvectors, etc. are, but I can't seem to place them in a quantum frame of mind. What do they mean in context? When I look these things up, I don't get an answer that makes much sense to me. They tell me how to find an eigenvalue but not what it really is.

I have been going through all my homeworks/exams from the first semester of this class to try and prepare myself for next semester, but I feel like I am trying to climb out of one of those grain silos; every time I try to learn more I just fall deeper into the hole of nothingness and death.

I love physics. But I need help.

 

[Orodruin]

For instance, I know what eigenstates, eigenvectors, etc. are, but I can't seem to place them in a quantum frame of mind. What do they mean in context? When I look these things up, I don't get an answer that makes much sense to me. They tell me how to find an eigenvalue but not what it really is.

They are not really anything more than what the mathematical description is. This is true of any mathematical tool, whether in quantum mechanics or classical physics. The physics part comes from making a connection between the mathematical description and measurements and observations that can be made in experiments. For example, the eigenvalues of the Hamiltonian represent energy states and the corresponding eigenvectors represent those states, which also are the states preserved under time evolution.

 

[mpresic3]

What book is your professor currently using, or is he/she teaching from his/her notes alone? Has the professor suggested some textbooks, including where he/she might be getting their problems out of? If you do not know what text is going to be the source of the material for the second semester, what text were you using the first semester. Often the professor uses the same text for the second one.

 

[vela]

I want to know what resources helped you in college quantum classes. I learn visually a lot better than verbally and would love any advice on videos/YouTubers/websites/simulations that help to visualize what is happening.

You can do yourself a favor by abandoning this idea of trying to visualize what is happening when it comes to quantum mechanics. Also, there is no evidence supporting the notion of learning styles.

For instance, I know what eigenstates, eigenvectors, etc. are, but I can't seem to place them in a quantum frame of mind. What do they mean in context? When I look these things up, I don't get an answer that makes much sense to me. They tell me how to find an eigenvalue but not what it really is.

You should be familiar with the postulates of quantum mechanics, and that's pretty much it. Again, abandon the misguided attempt to figure out what they "really mean." There's nothing to figure out.

 

[vela]

When I was in grad school, Sidney Coleman gave a talk at our colloquium. He pointed out that quantum mechanics is a more general theory than classical mechanics, so it makes sense to explain classical mechanics in terms of quantum mechanics, not the other way around. Much of the confusion students experience with learning quantum mechanics is from trying to make sense of quantum mechanics in terms of classical ideas.

 

[vanhees71]

You can do yourself a favor by abandoning this idea of trying to visualize what is happening when it comes to quantum mechanics. Also, there is no evidence supporting the notion of learning styles.You should be familiar with the postulates of quantum mechanics, and that's pretty much it. Again, abandon the misguided attempt to figure out what they "really mean." There's nothing to figure out.

I'm not sure, whether this is good advice. The state of mind of the student described in #1 pretty much reminds me of my own state of mind when first learning quantum mechanics. The main problem of quantum mechanics is indeed not so much to get the math, which I think is simpler to understand than the math in classical electrodynamics, because you deal with one scalar field (Schrödinger wave function) only for quite a time in the standard QM lecture, where you describe a single particle without or neglecting spin.

The main obstacle indeed is to gain a physical intuition behind the mathematical formalism, and this can only be achieved by thinking a lot about concrete physical (!) problems. The emphasis is on "physical", i.e., you should not get involved in all the philosophical discussions about the "interpretation of quantum mechanics". This you can do "for fun" later, but to begin with you should concentrate on the physics, and there the minimal statistical interpretation is all you need, and in my opinion it's all there "really" is in the sense of natural sciences "behind" the quantum-mechanical formalism.

The big didactical question is, how to most easily get this intuition, and I'm still not sure about the answer to this question. For me the eye opener fortunately was the introductory course lecture at university. After having learned quantum mechanics in high school from a very good teacher, who emphasized that she has to teach the then inevitable Bohr-Sommerfeld model for atoms, but that it's entirely wrong, and that the only true thing is "modern quantum mechanics", which she presented to us afterwards in terms of "wave mechanics", with the probabilistic interpretation of $|\psi(t,\vec{x})|^2$ as the probability distribution for the position of the particle ("Born's rule"). Of course, in high school we could learn only about the most simple examples like the particle in a box or the harmonic oscillator, but at least we got an idea, but no real understanding of quantum mechanics.

In the said theory-course lecture about nonrelativistic quantum mechanics (in our 5th semester of study) the professor used the then pretty new textbook by Sakurai and Tuan, Modern Quantum mechanics, which starts with spin 1/2 as the most simple case of a quantum system (nowadays called a q-bit). The problem with that approach, however, is that you don't really know what spin 1/2 is, and it can be really explained only later when it comes to the algebra of angular momentum and the rotation group and all that.

 

[mpresic3]

Sakurai's book is very good as a second or even third book/course in QM. It does not treat particle in a box, and some other foundational quantum systems. In that respect, Shankar's book is better. Shankar starts off slower, but I found it to be just as comprehensive in the long run as Sakurai, maybe with one or two exceptions. I think Shankar's book is underestimated. I also note that many sources of course notes online from University of Colorado, University of Illinois, years ago, (University of Rochester), give me the impression there is no one perfect textbook. Most professors rely on their course notes they developed over years of practice/presentation.