Should I Take Graduate Level Quantum Mechanics as an Undergraduate?

[tim_lou]

I'm currently an undergraduate majoring in physics. I will be taking intro. quantum mechanics next year, however, I wanted to take the graduate level one.

Before bashing me as one of those people who just want to skip around classes, hear me out.

I am in a REU program right now, and the project involves helium transition. So i thought, heck, I might as well study quantum on my own to understand what is going on. And if I am going to study, I might as well study the whole thing, and if I am going to study the whole thing, I might as well take the grad. level course next year.

I've thought about it for a long time and I decided to go for it.

I'm using Griffiths Intro. to Quantum Mechanics right now. I have started reading and doing problems couple weeks ago. I spent at least solid 6 hours on this subject every week (I don't count my hours, of course, but everyday, I would spend a reasonable among of time reviewing some material and go over a couple pages and then do some problems). my progress is about 1 chapter per 1.5 week (thought the one on hydrogen atom took much longer)

my math background is:
everything up to differential equation
introductory linear algebra
some proof course

my physics background is:
thermal
classical mechanics
modern physics
and introductory courses.

the undergraduate level quantum is an one semester 400 level course, the book we use is by Griffiths.
the graduate level quantum is a two semesters 500 level course (no prereq. for a grad. student) , the book we use is by Shanker.

I would like to know the typical subjects an undergraduate level quantum course covers.
ie. which chapters of the Griffiths book are essential? which ones are optional? which ones are not covered at all (except in the rarest case)?

and also, what is the general prereq. for a grad level quantum mechanics course (the first one). ie. What should a student know in order to succeed in a grad level quantum mechanics course?

plus,
looking at my progress (I'm on hydrogen atom and angular momentum right now), how likely am I going to finish the whole thing at the end of summer? (next semester starts at the beginning of September).

I just want an honest and realistic opinion,
thanks for reading this long post.

 

[Mororvia]

First, and you may have done this already, make sure your school will allow you to use the graduate quantum for your requirements... though I don't know why they wouldn't.

At my undergrad school there were 2 semesters of QM with the 1st semester being required. That semester covered chapters 1-4 in Griffiths plus some of the linear algebra in the appendix. The 2nd semester jumped around in Part 2 of the book, but covered both perturbation chapters extensively.

Unfortunately, my graduate course at a different school later essentially covered the same stuff as my 2nd semester QM in undergrad, but from a different book. I don't know if this is typical, and if its not, I feel a little cheated heh.

Anyway, if you're working through Griffiths now I imagine you could handle the graduate course without too much trouble. However, you may still benefit from taking the undergrad one since there could be important details that you've missed. Maybe you could communicate with who is teaching the undergrad course and see if (s)he thinks your progress is good.

Good luck!

 

[math_owen]

OK. Upfront I'm a math major, but I fancy myself as an aspiring mathematical physicist. And I have many friends in the physics department. Maybe though, with my years (30) I have some advise - I hope.

At my school, courses in EM and Waves/ Optics are also required as prereqs to Quantum. Maybe you've taken those and forgotten to list them. I'm not sure, but I have been told those are certainly necessary for understanding quantum.

Here's my opinion on the graduate courses, do it if you can. I'm a firm believer in over challenging yourself. Truly, it is always better than under challenging yourself.

This is tangential, but let me share the most painful experience you can ever have, IMHO. It's got a name, and it's beyond the pain of death and failure in my experiences. It's far worse. It's called the "shoulda-coulda-wouldas" and damn do they hurt if you catch a full blown case.

This is probably not a case of it, but starting down a path of being over conservative and not challenging yourself will most likely lead you to them. B/c someday, you'll get a shot, that proverbial one shot in a lifetime, and you'll be too afraid to fail, get hurt, etc, etc. and you won't do it. Then a decade down the road, you'll have had your heart ripped from your chest b/c you'll have finally fessed up and admitted to the mistake, and as the saying goes it's too late. There's a famous poem that partly addresses this some, "The Road Not Taken" by Robert Frost. Be sure you take your own path my friend.

If you're feeling froggy enough to teach yourself now, then even if you don't have the prereqs, I say do it anyway. You can always humbly step down to the undergraduate course after a couple of weeks. Or you can stick it out and take the bumps and bruises in stride. It could only make you strong if it doesn't break you. And being broken is only bad if you haven't the courage to get up off your ass after you've been knocked down.

Best of Luck!

 

[K.J.Healey]

I'd recommend asking the teacher what book is used in the advanced course and taking a look at it. Most likely the way it goes is : The undergrad course teaches the basics. The math is quite limited. The hardest thing you do mathematically is some ODE's I believe, and some matrix algebra. It covers a lot of material, and gets you in the QM mindset. You learn about BraKet notation, and commutators, and expectation values, wells, etc. All this stuff.
Then the graduate course is very similar. But since they expect you to know most of this already, they skip a lot of the explanation. The math (at least at my school) is a little more complex. This i think is undergrad:
http://www.lsr.ph.ic.ac.uk/~plenio/lecture.pdf
http://www.math.temple.edu/~prisebor/qm1.pdf
http://www.math.temple.edu/~prisebor/Advanced.pdf

This is grad (i presume)
http://www.ks.uiuc.edu/Services/Class/PHYS480/qm_PDF/QM_Book.pdfThere isn't THAT great of a difference, but when its a new topic the more difficult thought processes can be harder to follow.

 

[Brad Barker]

this past school year, i took the graduate level quantum mechanics sequence in place of the undergraduate version.

the differences were fairly minimal for quantum 1. the grad class covered, in addition to the material in the undergrad class, feynman path integrals, spherical tensor operators, and the wigner-eckart theorem.

it seemed like there was a pretty big difference between the quantum 2 classes. the graduate class covered the undergrad material in an entirely different chronological order, and much faster. we also spent some time on the dirac equation.

the grad class also had to solve problems numerically on a software package of choice, whereas the undergrad class did not.


i had a very strong mathematical background going in (had completed abstract algebra and complex variables before the start of my third year), and i did really well in the honors modern physics class. the deciding factor for me was that the prof for the undergrad class was the same as the honors modern class, so i'd have really just gotten more of the same for that first semester.

 

[tim_lou]

I'd recommend asking the teacher what book is used in the advanced course and taking a look at it. Most likely the way it goes is : The undergrad course teaches the basics. The math is quite limited. The hardest thing you do mathematically is some ODE's I believe, and some matrix algebra. It covers a lot of material, and gets you in the QM mindset. You learn about BraKet notation, and commutators, and expectation values, wells, etc. All this stuff.
Then the graduate course is very similar. But since they expect you to know most of this already, they skip a lot of the explanation. The math (at least at my school) is a little more complex. This i think is undergrad:
http://www.lsr.ph.ic.ac.uk/~plenio/lecture.pdf
http://www.math.temple.edu/~prisebor/qm1.pdf
http://www.math.temple.edu/~prisebor/Advanced.pdf

This is grad (i presume)
http://www.ks.uiuc.edu/Services/Class/PHYS480/qm_PDF/QM_Book.pdfThere isn't THAT great of a difference, but when its a new topic the more difficult thought processes can be harder to follow.

wow, the link you gave me really scared me a bit.
http://www.math.temple.edu/~prisebor/qm1.pdf
http://www.math.temple.edu/~prisebor/Advanced.pdf

specially the advanced one... relativistic quantum theory, field theory and quantum electrodynamics+ Dirac's equation...??! if that is the typical undergraduate course I'm pretty much screwed... but looks like none of that is in the Griffith's book though (the book we use for undergraduate course), so that is a relieve.

Ok, and it looks like that I will do reasonably well in the grad level course. So, as Owen said, I will go for it! it is better to try and fail than to surrender before the battle begins!

now, the next problem is... how the heck can I convince my department chair to let me skip the undergraduate level course...??

 

[cristo]

now, the next problem is... how the heck can I convince my department chair to let me skip the undergraduate level course...??

Well, get him to ask you a question off last years undergraduate course exam. If you give a satisfactory answer, then you have the prerequisite knowledge.

 

[ZapperZ]

wow, the link you gave me really scared me a bit.
http://www.math.temple.edu/~prisebor/qm1.pdf
http://www.math.temple.edu/~prisebor/Advanced.pdf

specially the advanced one... relativistic quantum theory, field theory and quantum electrodynamics+ Dirac's equation...??! if that is the typical undergraduate course I'm pretty much screwed... but looks like none of that is in the Griffith's book though (the book we use for undergraduate course), so that is a relieve.

Ok, and it looks like that I will do reasonably well in the grad level course. So, as Owen said, I will go for it! it is better to try and fail than to surrender before the battle begins!

now, the next problem is... how the heck can I convince my department chair to let me skip the undergraduate level course...??

How do you know that you have the knowledge of the undergraduate level QM? You mentioned that you're going through Griffith's text. What does this mean? Did you just go through the chapters and thought you understood it, or did you actually sat down, worked through the problem set, and got them all correct (assuming you know what the "correct" solution is)?

Remember, in physics (and mathematics as well), there is a difference between having only a superficial knowledge of the subject from simply reading it, versus actually understanding and having the SKILL to use it to solve actual problems. The latter can only be gained after working through and solving problems that apply the concept being studied.

Zz.

 

[tim_lou]

I'm not sure if it is that simple though... just one question and that's it? My friend went through great lengths to try to get the math department to let him take analysis and abstract algebra at the same time (he is one of the better math student and the department denied the request!). Hopefully, the physics department is nicer to undergrads.

 

[tim_lou]

How do you know that you have the knowledge of the undergraduate level QM? You mentioned that you're going through Griffith's text. What does this mean? Did you just go through the chapters and thought you understood it, or did you actually sat down, worked through the problem set, and got them all correct (assuming you know what the "correct" solution is)?

Remember, in physics (and mathematics as well), there is a difference between having only a superficial knowledge of the subject from simply reading it, versus actually understanding and having the SKILL to use it to solve actual problems. The latter can only be gained after working through and solving problems that apply the concept being studied.

Zz.

well, I try to derive all equations in the book (using the book as the guidance) (more exactly... re-derive, since I often fail deriving equations using my own method and then I would look the the book's approach) read the book, and work out most of the problems. It is impossible for me to do plain reading without falling asleep anyway (actually, when I can't fall asleep at night, I read Griffiths until I fall asleep) .

 

[cristo]

Hopefully, the physics department is nicer to undergrads.

I don't think it's a matter of the "department being nice," but more that the department doesn't want to allow students to take courses that they don't have the prerequisites for, as this will more often than not end in students failing!

I didn't mean that one question shows you know everything, but if you were asked one question off an exam paper, to which you replied with a more or less perfect answer, then I'd say you were ready to go straight to the grad course. If not, then you should take the undergrad course.

 

[K.J.Healey]

I'm actually in the same situation. I'm starting graduate school in the fall and since its a different university they want me to take their undergrad QM/TheoMech/StatMech/Thermo classes before I start the upper end ones. At first I was sort of upset, I had JUST taken those classes. But at this school they're considered graduate level. So basically I'll have to take:
Quantum Physics I (6000 level)
Quantum Physics II
Quantum Mechanics I (7000 level)
Quantum Mechanics II
Quantum Field Theory I (8000 level)
Quantum Field Theory II

Luckily they had notes online and what I'm finding is, I remember and KNOW about 80% of everything in the undergrad quantum. Its all your standard QM stuff.
But the 7000 quantum notes seems to assume I've learned something more, and I have a hard time following it. Something that's not in the 6000 QM notes. I don't know if there's ANOTHER class too, or maybe the notes don't reflect the actual full teachings.

In the end, the way I figure it is, its going to take me 5-6 years to get my PhD, if I have to shift some courses around and take classes for an extra semester or two so I can reinforce my basics then so be it. Whats another year if it will make me that much better of a Physicist, as well as make all the subsequent courses after the undergrad ones easier.

By studying yourself you may miss alot. You won't even know it until its too late. I'd recommend the basics. Take as many classes as you can, its never a waste of time. Don't be in a rush to learn the advanced material.

I remember in my senior year in undergrad I retook Calc 2 because it was my first math class in college (AP credits, so I took Calc2 freshmen year). I got a 80% in the class the first time I took it. That doesn't sound bad but at my school if your GPA was lower than 82% you were on probation. (I was always 90%+ total gpa)
But I retook Calc2 after taking Calc3, DiffEq, Boundary Value Problems, Linear, Numerical Methods, etc.
You think it'd be easy right? I can do standard calc stuff without thinking about it, the problem came when I had to remember how to derive simpson's 5/8ths rule, Taylor/Mclaren series, etc. I had no recollection of. I knew I was taught it once, but since I never used it in practice I lost it.

I guess my point is, there is a lot of material in undergrad courses.
Its very easy to remember 80% of it.
Its easy to master 50% of it, and remember 30% of it.
Its pretty hard, and takes a lot of work to master 80% of it.
And mastering 100% of it is near impossible on the first try. You just won't remember it all in a manner that it can be an effective tool. Thats the real issue. Looking at a problem and having no clue to begin, and then someone points out its just a thermal dissipation BVP, and you go "Oh yeah! I remember how to do that!" Is WAY DIFFERENT from knowing what to do, what tools you have when you approach a problem.

I know I'm ranting now. I'm just realizing some of this myself as I type in effort to reinforce my decision to retake the Undergrad courses this fall.

Sorry about the long post :) (and probably a lot of typos)

 

[Darkiekurdo]

This i think is undergrad:
http://www.lsr.ph.ic.ac.uk/~plenio/lecture.pdf
http://www.math.temple.edu/~prisebor/qm1.pdf
http://www.math.temple.edu/~prisebor/Advanced.pdf

This is grad (i presume)
http://www.ks.uiuc.edu/Services/Class/PHYS480/qm_PDF/QM_Book.pdf

Damn...

 

[K.J.Healey]

Maybe I was wrong about those books. Here at work I get bored easily and have nothing to do so i scour google for pdfs of textbooks. The ones I listed as undergrad i did so for the sole reason that I could understand them, and I only have an undergrad education in QM so far. Maybe I was wrong though.


EDIT: Turns out I think they're all for undergrad courses. I think the last one is just crazy advanced. Says its written for intelligent and diligent studenst who are basically driven to figure it out for the pure reason that they don't know about it. Its also supposed to segue into path integrals, etc.

 

[math_owen]

Hmmm...

Let's generalize shall we? We can categorize people like this; leader, follower, and rock. We don't need to consider the rocks, the case is trivial.

Of the other 2, the leader is far rarer, and believe it or not, this Western society, as much as it says it does, does not fully support them. And possibly this is good, because the best tend to emerge and say damn to the rules that guide the lemmings, I mean followers.

Seriously though. How many of the "greats" were self driven and self taught? Can I venture many if not almost most?

Our over PC, over protective, overly effeminate, outright broken and docile society tends to dislike and hold back the go getters. "You might get hurt, or even worse, oh don't say it, fail!" Whatever.

The real difference between graduate and undergraduate work is, as an undergraduate you're expected and forced into being a mindless lemming "as we sculpt your young minds" and it graduate school "we're paying your ass so you better damn well work hard."

If you can work hard, you're willing for the challenge and you're existential enough to deal with the consequences, and your school will let you jump up, then do it.

At my school, the physics department is very much this PC way. They made me repeat a freshman course b/c I missed a chapter, yeah a chapter in the course at another school. But, b/c that course was a 2 course sequence, and I didn't qualify for the 2nd semester, they made me jump into the 3 semester slow track physics.

The funny part was, I had already done independents in analysis, 2 algebras, and a probability. Which the math department accepted with open arms, and wanted me to jump up to graduate work right away, but I didn't and that was a huge mistake and a waste of a year for me. And I'm at a top math school - as well as a top physics school.

Lets analyze this further. I agree that it is important to know the basics, but thinking you can know 100% I would have to say is ignorant arrogance. That would show little understanding of intelligence and physics/math since all 3 are infinitely deep.

I believe though, that often the system does save those who are simply being stupid and trying to be show-offs from jumping into something they can't handle. And, it is possible that there are more of those than the genuine ones who want to really step up and work hard.

But, saving them while frustrating and holding back the self-starting future leaders is probably the worse of the 2 decisions. Holding back a leader for not hurting the egos of a handful of arrogant boastful followers doesn't seem right. Not to mention holding back the benefits for society.

Indeed, the best thing for those who would jump up for all the wrong reasons, is to jump up. It's that old school thinking of putting people in their place. Notice how we have a generation of spoiled me's running around because we've made parenting illegal. Hmmm... it's everywhere.

So, Tim, be warned, graduate school is indeed for the big boys, and all those around you there will have stronger incentives to do better than you. The grading, the work, and the competition will be fiercer.

But if you're a future leader, just step up, and don't ask. As for the followers, keep up the good work, and keep following.

Best of luck.

 

[K.J.Healey]

Lets analyze this further. I agree that it is important to know the basics, but thinking you can know 100% I would have to say is ignorant arrogance. That would show little understanding of intelligence and physics/math since all 3 are infinitely deep.

Just wanted to point out that I agree, and said it was nearly impossible. I was trying to make the same point when i said 100%.

But other than that your post may have changed my mind about retaking the courses. Its a tough struggle(in my situation) between having a free ride to learn as much as possible and as in depth as possible and benefit myself in the end, OR to actually challenge myself, maybe miss some things, but take that extra initiative and be ahead of the competition. I really have a hard time figuring out what's better in the long run, both career wise AND knowledge/abilit wise.

 

[math_owen]

I understand Healey I wasn't gunning you. I was pointing it out those who could read that someday and be possibly lead on to such a thing.

Healey I strongly suggest to you that you step up. The point of this "education" is far deeper than knowledge acquisition. It is to ultimately teach you to "teach yourself without guidance." Yes, that is it. The sooner you get it, the sooner you can take your place upfront.

Many people have fallen to the whole "knowledge acquisition" hole. It's about becoming a leader. It's about learning to learn without Big Brother holding your hand and telling you how to think.

Step up already my friend.

Best of luck.

 

[K.J.Healey]

Well, to be honest I already know how to teach myself. I learned how to do that during a 2 year internship at a national lab. Had to learn Fortran77, F90, C/C++ as well as the mathematics of crystalline structures. They basically said, "the library is over there, here is 10k lines of code, when you're ready to start working on it let us know" :) And so I spent a good 3 weeks learning the languages and mathematics (and throughout the internship too).

Thats not my issue. I have great confidence in myself in terms of understanding material. What I lack is the confidence in my ability to recognize WHAT I should understand. Theres no guide that says "To do well in Particle Theory learn this exact stuff:" And what I forsee as a problem for myself is if I happen to skip something that I didn't think of teaching myself.

One good example IS particle physics. I never had an undergrad class on it. Never thought I needed it. How was I to know? I get to studying for the Physics GRE and I think something like 15-20% is on particle physics. So then it was up to me to come up with a comprehensive learning plan for it, that includes everything they could ask on the test. But when you have no guide, its hard to know what's really important, and what would normally be skipped over as not-important.
Thanks to time always being a factor, its tough to know what to teach without some sort of guidance.

Actually, I did pretty well too my senior year. I asked the math department to teach me complex analysis and they set up an independent study where i met with a prof once a week and had an exam at the end. Surprisingly it went well at the time. I thought I had a firm understanding of the material, and I believe I got a 95% on the test.

I hope you see my point in this rant. That its not the material that is tough to learn by ones self but rather knowing WHAT to study. I guess the best course of action is to look up some school syllabi and try to follow it deviating whenever you feel necessary.

 

[ZapperZ]

well, I try to derive all equations in the book (using the book as the guidance) (more exactly... re-derive, since I often fail deriving equations using my own method and then I would look the the book's approach) read the book, and work out most of the problems. It is impossible for me to do plain reading without falling asleep anyway (actually, when I can't fall asleep at night, I read Griffiths until I fall asleep) .

So you know if the solutions that you arrived from the text's problems are correct? How?

Zz.

 

[math_owen]

I hope you see my point in this rant. That its not the material that is tough to learn by ones self but rather knowing WHAT to study. I guess the best course of action is to look up some school syllabi and try to follow it deviating whenever you feel necessary.

I see your point. Point well taken. You also gave yourself the first clue with looking up old syllabi.

Here follow this logic;

There is no one source. There is no one book. There is no one correct way. There is no one person. Etc.

What there is, is an infinite amount of stuff. Learning what to learn, is a matter of learning to recognize patterns. That IS the sovereign territory of the proverbial genius.

Look at many books. More importantly look at their tables of contents. Search the web for clues. But most importantly ask people. Try professors not teaching in your class too. For it is they who will be more honest with you. Better yet, ask students who have already had the class.

So. Recap.

Ask other professors the major points.
Ask students who have had the class the major points.
Launch your own library adventure into analyzing particle physics books.
Launch your own online investigation of particle physics.

But that's the point. Learn to learn. It's not about being apt at calculation, or apt at particle physics. It's being told there exists this territory that needs to be explored. No one has been there, you're the first. Tell me something about it.

Find patterns. Find relations. Find other sources.

Be your own guide.

Find courage to walk into the unknown.

And then,
DO IT!

 

[tim_lou]

So you know if the solutions that you arrived from the text's problems are correct? How?

Zz.

well, I wouldn't know 100% percent if I really got the problems correctly...and I admit that it is a problem not having the complete solutions. However, many of the problems are of the derivation type (with results already derived) and the more difficult calculation problems have solution included. Seeing how I have gotten correct results for most of the problems that have solutions included, I can say I'm fairly confident that I have gotten most of the other problems correctly.

 

[Dr Transport]

First of all, you do not need to know 100% of teh material. I would say that most schools would not let an undergrad skip the QM sequence and go straight to the graduate courses. I went to grad school with a person who didn't have an undergrad physics degree, but had a math degree. They thought that they could handle it, 3 weeks into the course they were underwater far enought that they ended up dropping and going back to take the UG courses. The undergrad course work is there for a reason, it gives you the basics so that you can go to advanced work and succeed not struggle.