Advise me how to learn Third year quantum Mechanics

[mrausum]

Hi, I'm going to have to have a fairly hectic 2nd year for my undergrad course. I'm accellarating and doing third year Quantum Mechanics and I'm therefore going to try and learn as much as i can before the start of the semester.

The course information is listed here:

http://www2.le.ac.uk/departments/physics-and-astronomy/extranet/student_area/module_info/module_specifications/PA3210.pdf

Which covers the first 150 or so pages of Quantum Mechanics by Alastair I M Rae:

http://rapidlibrary.com/download_fi...hanics+-+Modern+Mevelopment+4ed+-+A.+Rae+.pdf

I was wondering how i should go about learning the material. Should i just jump in and start reading the book? What Maths do i need before i start? Are there any better materials to learn from - 150 pages seems very short for a large-credit 3rd year course?

I'm basically looking for the most efficient way of learning the material to a reasonable standard. My marks get boosted by 20% because I'm accellarating, so i don't have to be as rigorous as if i was doing it in my 3rd year.

Any help appreciated. :)

 

[Landau]

My marks get boosted by 20% because I'm accellarating, so i don't have to be as rigorous as if i was doing it in my 3rd year.

Wow, I wish we had that.

The most important mathematics you will need, is linear algebra. Do you know it well?

 

[mrausum]

Wow, I wish we had that.

The most important mathematics you will need, is linear algebra. Do you know it well?

As in Matrices etc? No, i really don't know it well at all. I've read a bit, but i really haven't done them in any depth. What areas of linear algebra do i need to learn? Any video useful video lectures you know of? This seems to be good: http://video.google.com/videoplay?docid=7055571132713022746?

 

[maverick_starstrider]

As in Matrices etc? No, i really don't know it well at all. I've read a bit, but i really haven't done them in any depth. What areas of linear algebra do i need to learn? Any video useful video lectures you know of? This seems to be good: http://video.google.com/videoplay?docid=7055571132713022746?

You're going to need to know it MUCH better. Inner product spaces, dual vectors, hilbert spaces, etc.

 

[mrausum]

You're going to need to know it MUCH better. Inner product spaces, dual vectors, hilbert spaces, etc.

The majority of the people on my course are doing it in the 2nd year. And in the first year we haven't studied anything advanced like that. It's only been very basic maths with a bit on matrices. Are you sure i'll need all that Maths? And if so, what should i learn from?

The blurb on the back of my quantum mechanics textbook says "students who have completed the first year of their course will find this an easy-to-understand guide to the basics of quantum mechanics". I linked to a .pdf of the textbook in my original post, so maybe you could check that and verify that i do indeed need all the maths you mentioned (i'm only doing the first 7chapters).

 

[Landau]

Matrix calculation is the least you need to know, like calculating eigenvalues/eigenvectors, diagonalize and invert a matrix, etc. But you should also have a nodding acquaintance with basic concepts like linear dependence, basis, span, linear map, operator,... I'm sure you covered that in a linear algebra course?

Of course, it depends, but I can't imagine a 3rd year QM course not heavily using matrices, bases, inner product, etc.

Go to page 113, does it make any sense to you?

 

[mrausum]

Matrix calculation is the least you need to know, like calculating eigenvalues/eigenvectors, diagonalize and invert a matrix, etc. But you should also have a nodding acquaintance with basic concepts like linear dependence, basis, span, linear map, operator,... I'm sure you covered that in a linear algebra course?

Of course, it depends, but I can't imagine a 3rd year QM course not heavily using matrices, bases, inner product, etc.

Go to page 113, does it make any sense to you?

We didn't do a first year linear algebra course. And by the looks of it, we don't do it in the 2nd year either. :/

 

[Landau]

Hmm...that's a bit unconventional. Any physicist should know linear algebra. Anyway, browsing through your book, it may be not that bad.

It is based
on a course of about thirty lectures given to physics students at the University
of Birmingham towards the beginning of their second year—although, perhaps
inevitably, the coverage of the book is a little greater than I was able to achieve
in the lecture course. I have tried to develop the subject in a reasonably rigorous
way, covering the topics needed for further study in atomic, nuclear, and solid
state physics, but relying only on the physical and mathematical concepts usually
taught in the first year of an undergraduate course. On the other hand, by the
end of their first undergraduate year most students have heard about the basic
ideas of atomic physics, including the experimental evidence pointing to the need
for a quantum theory, so I have confined my treatment of these topics to a brief
introductory chapter.

Maybe your course teaches all the necessary mathematics itself.

 

[mrausum]

yea, the part where he says "relying only on the physical and mathematical concepts usually
taught in the first year of an undergraduate course.", fills me with hope that i can actually learn from this textbook.

 

[ice109]

Wow, I wish we had that.

The most important mathematics you will need, is linear algebra. Do you know it well?

i don't understand why in the world people say this. the most important mathematics you will need is functional analysis on hilbert spaces. linear algebra is vaguely in there. eigenvectors/eigenvalues are sturm-louville theory - they were invented for analysis of pdes. besides finding an eigen decomposition of a system is easy, understand what it means for a basis to span a space is also easy but solving pdes is hard.

 

[Landau]

Of course the mathematics behind QM is functional analysis on hilbert spaces. But for functional analysis, you'll need linear algebra anyway. The most important reason why I said that: in 3rd year QM, students will never hear about functional analysis. Usually what they're told is: "you know this and this from linear algebra in finite-dimensional vector spaces. Now, we just pretend this all works in our infinite-dimensional hilbert space, and if it doesn't, we'll tell you." In a physics bachelor, mathematical formalism is hardly ever stressed.

And I hope you agree that someone who doesn't know how to add two matrices isn't ready for a second QM course.

 

[mal4mac]

Do you need Hilbert spaces for the first 150 pages of Rae? Why not just read Rae then you will know exactly what you need! So yes! Just jump in and start reading the book...

 

[mrausum]

Do you need Hilbert spaces for the first 150 pages of Rae? Why not just read Rae then you will know exactly what you need! So yes! Just jump in and start reading the book...

No. As far as I can see we only need to know about eigenvectors, eigenvalues and a bit on matrices. The book's aimed at 2nd year students, and like a lot of you have mentioned, my tutor says a lot of the maths is just taught as you go along in the book.

I quickly read the first 40 pages last night, and it was fairly easy to understand. Most of it's just linear differential equations and stuff we did in the first year - harmonic oscillators, infinite wells etc. I think i will have to learn my matrices properly for later on though.