Undergraduate or Graduate Quantum Mechanics?

[Phyzwizz]

I am an undergraduate student and I am currently trying to decide whether to take undergraduate or graduate Quantum Mechanics. I plan to do a PhD in physics later on, so I assume that I will eventually take a graduate course in Quantum Mechanics, so I figure I might as well take it now, being that there are only math and physics prerequisites for which I have completed. The only trouble is whether I will be able to handle the course at the same level as the undergraduate course because I most certainly will not. So another question I had was whether when applying to graduate school, in general a lower grade in a graduate course is looked at as better than a higher grade in an undergraduate QM course. I'd just like some general advice on what would be better for learning (greater challenge more learning?) and what would be better for a future career and graduate school prospects.

 

[Vanadium 50]

The only trouble is whether I will be able to handle the course at the same level as the undergraduate course because I most certainly will not.

Taking a class that you are not prepared for is unwise.

 

[gmax137]

Taking a class that you are not prepared for is unwise.

Listen to V50.

I left physics a long time ago, so I could be wrong but I think you're better off taking more 'advanced' classical mechanics (with Lagrangian & Hamiltonian approaches) before you go into the graduate QM.

 

[ZapperZ]

I am an undergraduate student and I am currently trying to decide whether to take undergraduate or graduate Quantum Mechanics. I plan to do a PhD in physics later on, so I assume that I will eventually take a graduate course in Quantum Mechanics, so I figure I might as well take it now, being that there are only math and physics prerequisites for which I have completed. The only trouble is whether I will be able to handle the course at the same level as the undergraduate course because I most certainly will not. So another question I had was whether when applying to graduate school, in general a lower grade in a graduate course is looked at as better than a higher grade in an undergraduate QM course. I'd just like some general advice on what would be better for learning (greater challenge more learning?) and what would be better for a future career and graduate school prospects.

This question is one of the most puzzling questions I've seen on PF.

1. What makes you think you have the knowledge to skip undergraduate QM and jump straight into graduate level QM? If undergraduate QM is not needed, why do you think all schools offer it?

2. Have you talked to your advisor and/or the course instructor and get their opinions? They, of all people, know not only the level that these courses will cover, but will have some knowledge on the level that YOU know.

3. Have you opened the text used for the undergraduate QM class and tried to do a few of the HW questions? You do know that you ARE expected to know the material covered in such a text BEFORE enrolling in the graduate level class. They may not state it explicitly in the requirement or prerequisits, but I'm sure that was because they didn't think anyone was nutty enough to skip undergrad QM to jump straight into grad level QM class.

Zz.

 

[Phyzwizz]

1. The graduate QM course does not have a requirement of having taken the undergraduate QM course. For the undergraduate B.S. of "Mathematics and Physics" it is actually suggested to take the graduate course for this major.
2. I spoke with the course instructor and he said that the assignment level is quite high, but there are other undergraduates in the course.
3. I have opened the undergraduate text and being an undergraduate text, its mathematical explanations amount to a lot of hand waving in the giving of different formulae (as in the explanations are not even close to mathematical proofs and are attempts instead to describe what is happening in words). Obviously there are some formulae in physics that can't be derived purely from mathematics, but for those that can have parts or the whole derived this way are ignored in the book.

 

[jtbell]

3. I have opened the undergraduate text

Out of curiosity, which book is it, and which book is being used in the graduate course?

(added)

For the undergraduate B.S. of "Mathematics and Physics" it is actually suggested to take the graduate course for this major.

Instead of the undergraduate QM course, or in addition to it?

 

[micromass]

2. I spoke with the course instructor and he said that the assignment level is quite high, but there are other undergraduates in the course.

Do you know of such people who did not do undergrad QM? How did they do?

3. I have opened the undergraduate text and being an undergraduate text, its mathematical explanations amount to a lot of hand waving in the giving of different formulae (as in the explanations are not even close to mathematical proofs and are attempts instead to describe what is happening in words). Obviously there are some formulae in physics that can't be derived purely from mathematics, but for those that can have parts or the whole derived this way are ignored in the book.

Making quantum mechanics mathematically rigorous is possible, but very very difficult. It requires grad level knowledge in mathematics. Furthermore, making it rigorous is pretty useless from a physics point of view. It does not help making physical predictions.

I really doubt that the grad course will be more rigorous with respect to mathematical proofs either...

 

[Phyzwizz]

I only really know of undergrads who are currently taking the course.

In the long run, should one not develop a mathematically rigorous understanding of the physics in order to make extrapolations from current knowledge or is this really not how important theoretical physics research is done? How exactly Theoretical Physics research is conducted is a mysterious point to me actually. I believe it is predominantly mathematical today, with snippets of more ambiguous physical intuition to make the leaps and bounds.

I have viewed the first homework for the course and there are problems which deal with mathematical proofs for needed forumulae, but these appear more concerned with Dirac and other notation.

The undergraduate book is Griffith's "Introduction to Quantum Mechanics" (Seems too straightforward and simple, and like the only real challenge for the course will be in memory, not in problem solving. Perhaps this changes later on in the text, I wasn't able to tell)
The graduate books are Shankar's "Principle's of Quantum Mechanics"
Sakurai's "Modern Quantum Mechanics" and Weinberg's "Lectures on Quantum Mechanics"

It is proposed that undergraduates with the aforementioned declared B.S. may take the graduate course instead of the undergraduate (I have confirmed this with the professor for the graduate course).

Part of the reason, I'd like to switch, is also because the teacher for the undergraduate course, doesn't seem all that great in that he is foreign (difficult to understand his speech) and really just writes equations on the board, and goes through very basic examples, whereas the professor for the graduate course is understandable in speech as well as a lot more challenging in all aspects, which I think is good for learning in general. I've read a number of cognitive science research articles describing the benefits of having particularly challenging material (in the end you learn a lot more). Although I don't want the course in the end to be a scar on my transcript.

 

[vela]

Like the others, I'm puzzled by the suggestion to take the graduate quantum mechanics course without having taken an undergraduate course. You can definitely learn more from a challenging course but that's if you're adequately prepared for the challenge.

 

[Vanadium 50]

It is far, far better to get a solid handle on QM at the level of Griffiths than a cursory understanding at the level of Shankar. And while there is something to the idea of challenging yourself, you wouldn't take French III as your first exposure to French.

 

[porcupine137]

What school?

It's hard to know what to say without knowing that. The fact that they apparently suggest that you take the grad version maybe means that you should? Hard to say. Knowing the school might help a bit.

 

[WannabeNewton]

In the long run, should one not develop a mathematically rigorous understanding of the physics in order to make extrapolations from current knowledge or is this really not how important theoretical physics research is done?

Not even in the slightest.

I believe it is predominantly mathematical today, with snippets of more ambiguous physical intuition to make the leaps and bounds.

Incorrect.

The undergraduate book is Griffith's "Introduction to Quantum Mechanics" (Seems too straightforward and simple, and like the only real challenge for the course will be in memory, not in problem solving. Perhaps this changes later on in the text, I wasn't able to tell)

It's very easy to look at something with a cursory glance and convince yourself that it's easy. When you actually sit down and try to work it out then you'll be quickly unconvinced of that.

It is proposed that undergraduates with the aforementioned declared B.S. may take the graduate course instead of the undergraduate (I have confirmed this with the professor for the graduate course).

Well if it's recommended by the department then you should follow their mapped out course sequence. These kinds of things are very different across universities so if your department really does suggest that then you would probably be better off following its advice. At my university for example it would be suicide to take graduate QM before having an undergraduate course on it.

 

[porcupine137]

I only really know of undergrads who are currently taking the course.
How exactly Theoretical Physics research is conducted is a mysterious point to me actually. I believe it is predominantly mathematical today, with snippets of more ambiguous physical intuition to make the leaps and bounds.

I'm not so sure about that. It's hard to make leaps and bounds just focusing on pure math.

 

[dipole]

I never took an undergrad course in QM - I took it at the graduate level in my senior year. That being said, I wouldn't recommend it - you'll want to see the stuff a few times, since some of the concepts take a lot of practice and time to really sink in.

 

[jtbell]

you'll want to see the stuff a few times, since some of the concepts take a lot of practice and time to really sink in.

This applies to any of the core subjects in physics. Most people benefit by going through the material more than once, at different levels of sophistication. I studied QM three times: first as a quick introduction to the wave function and the Schrödinger equation in a second-year "intro modern physics" course; then in a third/fourth-year undergrad course; then in graduate school.

(Then again when I taught an undergraduate QM course.)

Similarly for E&M, classical mechanics, and thermodynamics.

I suppose some people can master the material in one go, in a graduate course, but I suspect there are rather few of them.

That said, if it is in fact common practice at your school for undergraduates to start with the graduate course, and you feel up to it, then it will probably work out OK. Just don't expect to get out of taking QM again when you go to grad school, except maybe if you stay at the same school.

 

[Phyzwizz]

Thanks for all the advice, I've decided the best thing is probably just to take the undergraduate course now, since I'll have to take the graduate course eventually anyways.

 

[ZombieFeynman]

When I took QM at the undergrad level (Griffiths) I found it too easy. And I think that I learned more than if I found it hard. Because the content required for the class was easily done, I was able to do all of the problems in Griffiths and really sit and play with the material. I may have survived graduate QM the first time around with my GPA intact, but maybe not. I certainly think that when I did take graduate QM (in grad school!) having really played with and understood QM very well at the Griffiths level help me a lot.

I think the very well motivated undergrad benefits a lot from taking easier classes sometimes. You can ramp up the difficulty on your own without the stress of monstrous exams. If you feel that the course is too easy, make it harder for yourself.

 

[radium]

I actually went straight to grad quantum and had no problem at all. It was a great decision for me personally as I loved the class, learned a ton and it also significantly accelerated my research in condensed matter theory.

However, the reason I was able to skip undergrad quantum is that I had learned a lot through my research with the help of my grad student mentor and by myself. I had read through a combination of Griffiths, Shankar, and Sakurai the previous summer pretty thoroughly so I actually did not have much difficulty following the course.

 

[zif.]

3. I have opened the undergraduate text and being an undergraduate text, its mathematical explanations amount to a lot of hand waving in the giving of different formulae (as in the explanations are not even close to mathematical proofs and are attempts instead to describe what is happening in words). Obviously there are some formulae in physics that can't be derived purely from mathematics, but for those that can have parts or the whole derived this way are ignored in the book.

The mathematics is not anywhere near the important part of QM. New concepts and knowing when to do what is what is important. Do you remember the first time you were introduced to linear algebra? None of the mathematics involved is very hard, but you still need to know *what* to do, not just *how* to do it. You have to learn a whole new algebra for QM. How much experience with spin do you have? I can't recall any undergraduate courses that involved spin other than QM and intro to particle physics (which required intro to QM).

What does 1/2 + 1/2 equal to you?

1?

or

0 and 1?

Do you know when to use either result?