The Mathematics of Quantum Mechanics

I have been posting a lot in the quantum mechanics thread started by ryans lately. Most of my questions, however, relate to learning/understanding the mathematics of quantum mechanics. So i decidied to start a new thread that focuses more on the math.

To start out, I was wondering about a few books.

There is one I found called "Schaum's Outline of Quantum Mechanics " It is not very expensive and looks like it covers a lot of stuff. Has anyone heard of these "Schaum's Outlines"? He has a book for almost every advanced area of mathematics and physics you can think of. Are they good books? I also found some books called things like "problems in quantum mechanics" I think maybe those would help me out.

I will have some questions about specific math related things shortly. Hopefully some other people will find this thread of use and be able to better understand the abstract nature of higher mathematics.

 

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Schaum's outlines are good for an introduction. I happen to posses Schaums Outline Series - Theory and Problems of Advanced Calculus © 1963 and also Schaums Outline Series - Theory and Problems of Complex Variables © 1964. They are fairly decent, I dont know what any more recent publications are like these days.

 

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I've got an ancient Schaum's Outline for College Physics...still in foot-pounds and everything

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from what year?

 

Personally I use 'Quantum Mechanics' by Alstair Ray, which is mainly mathematics, with some abstract explanation thrown in. Unfortunately it expects you to know some of the mathematics already so without another maths book on hand it might be tricky to follow.

 

right now i have around 5 books on these advanced mathematics.

I have Quantum Theory by David Bohm, Mathematics of Classical and Quantum Physics, and Pronceton Guide to advanced physics.

I have some other books focused on just math stuff too.

I can figure out lots of it from these and online sources, its really just a matter of going through it and trying some problems out and then seeing if i did it right.

 

The way most American physics majors start in QM is by taking a course based on a book such as Introduction to the Structure of Matter by Brehm and Mullin or Quantum Physics by Eisberg and Resnick. The mathematics in those books is restricted to calculus and differential equations. In parallel with that, students take linear algebra so that they can learn the Hilbert space formulation of QM in a more advanced course, based on a book on the level of Liboff, Griffiths, or if you're really ambitious, Sakurai.

 

So then, since I can't take a class real soon, but since i am at the level of differential equations and linear algebra perhaps I should get one of these books that use stricly calculus and differential equations as oppose to learning about hilbert space and inner product space and all that other stuff. Would you agree to this? If I am going to do that then I am guessing the recommened book would be Introduction to the Structure of Matter or the other one you mentioned? Any other suggestions from anyone else or you tom2 about a book of this sort? In a few days/weeks I will start posting actaul math questions. It is just a matter of whether I go for the books you suggested or use the ones I have and internet sources to learn the other way.

 

i would also highly recommend griffiths introduction to quantum mechanics as a starting point.

 

thanks for the recommendation lethe. I found it for like $60 on amazon. Know anywhere i could get it cheaper? Also, I was wondering if everyone would recommend the feynman lectures on physics...i have been meaning to buy those for a long time now.

 

i don t think the feynman lectures are a good way to learn quantum mechanics.

 

Quantum mechanics problem from a textbook

Hello everyone. I started this thread months ago when I was going to start teaching myself quantum mechanics. Needless to say I didnt get around to it right away. Now that I have finished my differential equations course and have some extra time (and some better books) I have began to work on learning it. I got both Liboff and Griffiths through an inter library loan and now I actaully feel like I am learning and understanding the stuff.

And now for the problem. I just need someone to tell me if my answers are right to this problem since no answers are given. If it is wrong, don't bother going through how to get the right answer, I will just recheck my work.

(This is from Griffiths, problem 1.14)

A particle of mass m is in the state

Ψ(x,t)=Ae^-a[(mx^2/h)+it]

where A and a are positive real constants.

(a) Find A

My answer: A=(2am/(h&pi

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)^(1/4)

(b) For what potential energy function V(x) does Ψ satisfy the Schrödinger equation?

My answer: V(x)=2ma^2x^2

(c) Calculuate the expectation values of x,x^2,p, and p^2

My answer: <x>=√(h/(2am&pi

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)
<x^2>=h/(4am)
still have to do p and p^2

If anyone would also happen to have a link to solutions from griffiths books that would work just as well.

 

Re: Quantum mechanics problem from a textbook

yes, this is what i got.

this is not what i got. I have an additive constant (can we neglect that? i don t think so, but i m not sure why not), but also i have some factors of 2*pi since the hbar from Schrödingers equation don t quite cancel with the h in the wavefunction you gave me. i guess when i go back home in a few days, i will check in my copy of griffiths to see if i copied it correctly.

i will check your expectation value calculation as well.

sorry it took me so long to reply to this thread. i think i missed it at first.

 

lethe,

thank you so much for the response. I think the h in the equation i gave is actaully supposed to be h-bar, but i am not sure. I will double check it soon. I will have more questions soon. thanks again.

 

That should read:


a) Your answer is correct if you replace h with hbar

b) Your answer is correct

c) < x > = 0 (odd integrand)

< x^2 > = hbar/4am

< p > = 0

< p^2 > = amhbar

Doesn't the problem also ask for (sigma x), (sigma p) and (sigma x)(sigma p

 

yes. i think i monkeyed it up before. cephas answer is correct.

 

Thanks for double checking it Sacroiliac. You are correct, the problem does also ask for the uncerntainity in x and in p. I just hadn't done that yet.

Could someone also please tell me how to make subscripts and superscipts. I don't know how to do that.

 

L&lt;sub&gt;x&lt;/sub&gt; gives you a subscript: L_x
x&lt;sup&gt;2&lt;/sup&gt; gives you a superscript: x²

 

ah, ok that was easy. thank you.