Just how much math do you need to know to take an introductory QM course?

[Odyssey]

I am currently taking an introductory QM course...well, first...I find my prof is of no help at all...he's really bad at explaining concepts...and can't even speak English. So...I am basically learning on my own. I understand the stuffs he talk in his lectures, but when the assignments come, the questions have nothing to do with what he talked about.

Well, to my point...just HOW MUCH math do you need to know BEFORE taking an intro QM course?? I already finished vector calculus (so I guess that's end of 2nd year calc for the standard uni level)...also I finished an intro to DE course...and an intro to linear algebra. But when I look in a QM textbook...the math comes out of nowhere...it's very frustrating.

I do find the tutorials on this forum on QM very helpful...it's actually where I learn about QM.

 

[jtbell]

Which textbook does your course use? Ordinarily I'd say that your math background should be suitable for introductory QM. Your textbook should explain things that go beyond partial derivatives, basic differential equations, and basic linear algebra. Your university's (or professor's) idea of an "introductory QM course" may be different from mine, of course.

Can you give some examples of the kind of stuff that you're getting stuck on, in your assignments?

 

[Integral]

The only thing I see that you are missing which would be helpful is some knowledge of Partial Differential Equations.

 

[Thrice]

Physics-math is different from math-math. Quite another thing altogether. Try a different textbook.

 

[Odyssey]

The textbook I am using is Quantum Mechanics by Robert Scherrer. As for the homework is concerned...I am stuck on the Fourier transform...and solving the Schrodinger Equation.

As integral said...the thing I am missing is partial differential equations I guess...are there any good sites around so I can quickly pick up on that?

 

[complexPHILOSOPHY]

The other thing which Thrice mentioned is that you aren't doing pure mathematics, you are applying mathematical theories and applications to physics so it because a bit more disconnected then the mathematics itself in the sense that you have construct a functional relationship between the two.

I like to work through alternate texts in conjunction with the one required or recommended to get a better idea as to what is going on. If you are having problems, send these guys examples like they asked or pose your questions on the homework forum.

I am only in my first physics sequence so I can't comment about QM but I have read that it essentially will deconstruct into linear operators in hilbert spaces which requires the use of hardcore analysis and some other abstract mathematics.

Have you worked through any higher level abstract algebra involving fields, rings, groups, vector spaces, etc.? I know you did intro LA but I am not sure how much other branches of abstract algebra it exposes you to.

Would working through this be benficial to him? I am just throwing ideas out since I am pretty useless in the QM knowledge department.

 

[rbj]

The only thing I see that you are missing which would be helpful is some knowledge of Partial Differential Equations.

what about probability and random variables? knowing stuff like distribution functions, p.d.f.'s, expectation values, moments...

 

[ptabor]

Go to your uni's library and pick up a copy of Griffith's intro to QM - this book has a wealth of examples and problems with a wide range of difficulty.

To learn the mathematical techniques, such as pde's, distribution functions, etc.. I would highly recommend Boas' book Mathematical Methods in the Physical Sciences.

 

[jtbell]

The textbook I am using is Quantum Mechanics by Robert Scherrer. As for the homework is concerned...I am stuck on the Fourier transform...and solving the Schrodinger Equation.

I haven't seen that book myself, so I can't comment on it or give specific tips, unfortunately.

As a general tip, try looking in your university's library for other QM books that you can borrow to use as backup references. Different books assume different levels of mathematical background from the student, have more or fewer worked-out examples, put different emphasis on different topics, etc. Browse through them until you find one or two that seem to suit you.

A lot of second-year "modern physics" textbooks also have some basic QM, and usually don't assume the student knows much math to begin with. They introduce the idea of separation of variables to solve partial differential equations, etc.

 

[Odyssey]

Thanks for the advice. I'm going to visit my library tomorrow to see what I can get...will try to check out Griffith's intro to QM, Boas' book Mathematical Methods in the Physical Sciences, and another book on modern physics.

As for the LA I got...it's introductory stuff...no rings, fields, groups yet. I got some beginners exposure to vector spaces...

My assignment is due on Thursday. It has questions like expanding the initial wave function in terms of its energy eigenfunctions and finding the time evolution of the wave function...but...don't really know how to get started yet.

 

[complexPHILOSOPHY]

If you are ambitious, I would pick up Herstein's "Topics in Algebra" which was recommended to me. My math level is Calculus I so far, but I have had no real problems working through it indepently.

It covers some nice topics (sets, groups, rings, fields, vectors, etc.)and introduces you to a lot of the language present in modern mathematics. I have looked through Galois Theory (soooo beautiful and elegant) but am not at the level to appreciate it yet.

It's all very beautiful math regardless of it's applications (even though it is full of applications).

I am a math nubbbbb so perhaps someone here can give you better advice.

 

[chemisttree]

You might also want to consider a text on computational chemistry. The theory and applications are presented together giving context and example to what is otherwise a very disconnected course.

The math doesn't really come out of nowhere, it just seems that way.

Try looking at Errol Lewars book titled "Computational Chemistry - Introduction to the Theory and Applications of Molecular and Quantum Mechanics".

I had a professor with a thick polish accent. I still remember most of my Physical Chemistry with that accent...

 

[arunma]

I am currently taking an introductory QM course...well, first...I find my prof is of no help at all...he's really bad at explaining concepts...and can't even speak English. So...I am basically learning on my own. I understand the stuffs he talk in his lectures, but when the assignments come, the questions have nothing to do with what he talked about.

Well, to my point...just HOW MUCH math do you need to know BEFORE taking an intro QM course?? I already finished vector calculus (so I guess that's end of 2nd year calc for the standard uni level)...also I finished an intro to DE course...and an intro to linear algebra. But when I look in a QM textbook...the math comes out of nowhere...it's very frustrating.

I do find the tutorials on this forum on QM very helpful...it's actually where I learn about QM.

If you've had courses in linear algebra, differential equations, and vector calculus, then you should be good to go. However, I must say that Thrice was right on the money. Physicists do math a lot differently than mathematicians. I have a second degree in math, but to be honest, most of the math I know I learned in physics. Someone else mentioned checking out David Griffiths' book on quantum mechanics. I would agree with that; he explains things very well, and writes in a very conversational tone. If your library has Griffiths, you might want to check it out.

what about probability and random variables? knowing stuff like distribution functions, p.d.f.'s, expectation values, moments...

No, I wouldn't say that's necessary for a senior level undergraduate quantum course. I took probability theory (after quantum, actually), and the approach was extremely different. Mathematicians spend a lot of time covering the formalism of probability theory, but physicists really strip the subject down to the bare bones in applying it to quantum mechanics. For example, one doesn't need to know anything about distribution functions or moment generating functions to study quantum (though these are important topics in their own right). Pretty much all you need from probability is p.d.f.'s and expectation values. Physicists can cover this in about half an hour, whereas mathematicians might spend a whole week on it. It's not that the mathematician's approach is wrong, it's just that math students need to study these things in much greater depth than we physics people do, so we can afford to skimp on the rigor.

A course in probability theory is great in its own right. But if your plan is to study quantum mechanics, then you don't need to worry about it.

 

[shirazu]

The Boas book suggested is really excellent. Most math courses you might end up taking are going to teach you a bunch of really silly math theory, which may or may not, with emphasis on may not, ever help you in actual physics. After calc you would be better off trying to find a good physics math methods course for one or more semesters. For example I took DE and math methods in the same semester, and practically everything I use I learned in math methods, even though the methods class only talked about DE for 3-4 weeks and the DE was a semester course. The exception is if your school's math department is focused on engineering and the like, then you might have a better experience.

 

[complexPHILOSOPHY]

Why are the mathematical theories silly, just curious?