Need to Learn Quantum Mechanics Fast? Tips for REU Success!

[Dahaka14]

I'm in a tight spot. I got accepted to an REU to do an atomic physics project using the Hartree-Fock method, and I just finished my first year in physics. I'm pretty advanced, but I've never taken a class on quantum. My other research advisor told me to read through Griffiths and that I'd be good to go. I'm near the end of the second chapter already (on harmonic oscillators). Any advice on what to read or do in the next couple of weeks before I go to my REU site to learn quantum and perturbation theory quickly?

 

[maverick280857]

Does your REU site teach perturbation theory "quickly"?

I don't have an opinion on this, as I am still (and always will be) learning QM. In short, IMHO, there is no quick way to learn quantum mechanics. A project may be a good chance to learn QM in the first place, but you probably won't get a good taste of it. For example, the basic principle behind perturbing the Hamiltonian isn't very difficult, but if you really want to understand it you have to solve problems. If you do things quickly you probably won't have time to solve problems and test the theory.

I would say read Griffiths and other books you can find in your library. But just don't read them as story books...solve problems and get stuck, so you can learn something. Work on the project alongside, there's no harm in doing that. You might want to check out this book: https://www.amazon.com/dp/058235692X/?tag=pfamazon01-20. Its a standard text and most likely your library has a copy. Good for both Perturbation Theory and Hartree Fock, esp if you're starting out.

 

[BioCore]

If you just finished your first year and the REU site knows about this I am sure they will not expect you to know a lot of QM or be an expert - as that would just make you a genius in their eyes.

 

[G01]

If you just finished your first year and the REU site knows about this I am sure they will not expect you to know a lot of QM or be an expert - as that would just make you a genius in their eyes.

I agree. I doubt they expect you to be an expert in what the are doing. If they are, then they should not be looking for first year REU Participants. You'll be fine. Keep doing what your doing and learn quantum mechanics at a pace where you can absorb it and do problems. Don't rush through the learning process. Good luck to you!

 

[Dahaka14]

Thanks guys, I'll look into that book maverick posted. Believe me, I understand how I shouldn't read them like storybooks. I did that for awhile, and worked my way through higher level stuff without doing problems, and then my most recent research professor asked me to solve some basic problems for him, and I couldn't do it! You are absolutely right, and thanks for the advice!

 

[maverick280857]

Thanks guys, I'll look into that book maverick posted. Believe me, I understand how I shouldn't read them like storybooks. I did that for awhile, and worked my way through higher level stuff without doing problems, and then my most recent research professor asked me to solve some basic problems for him, and I couldn't do it! You are absolutely right, and thanks for the advice!

I'm sure you'll do great. The fact that you have landed with a project of this nature right after your freshman year is indicative of the confidence your REU judges/supervisors have in you. [Sidenote: Personally, I believe its possible to learn QM given your background (I myself started taking an interest long before my freshman year and that helped me learn a lot of neat techniques which helped in various other courses) but perhaps others may disagree.] So, just enjoy yourself, read whatever interests you...there are so many QM books out there. Ask lots of questions and solve problems. You will be fine.

Good luck!

 

[Dr Transport]

Check out the Schaum's outline in QM...

 

[Pythagorean]

What I studied in my two semesters of Undergrad in QM using GRIFFITHS, SECOND ED.:

(note: Linear Algebra is helpful to understand some of the basic concepts of QM.)


Schroedinger TIme-Dependent Equation:

get a good feel for how to handle the basic potential wells (infinite, finite, ones when d(Psi)/d(x) is not continuous),

know the difference between scattered states and bound states in the wells, (and how they relate to discrete and continuous spectra of eigenvalues, CH 3.3 Griffiths).

The harmonic oscillator (eek!), (extra credit: think of when and how to apply ladder operators)

Formalism (ch. 3)

Bohr's three postulates (Observables: (3.1, 3.2))

Statistical Interpretation (3.4)
Uncertain Principle (3.5)

CH. 4, QM in 3D

Read and understand ALL of the general ideas in this Chapter. It leads up to the the atom, and an interesting consequence of having a third dimension... (I'll leave the surprise for you, you'll recognize the quantities that come out of 3D I'm sure, they're quite popular).

When you read this chapter, don't get caught up on trying to memorize all the tables it has. If you took Electrodynamics with Griffiths, you should have a basic understanding of spherical harmonics and all that Legendre jazz.

CH 5, Identical Particles

We only did 5.1 and 5.2 here. The concept of Identical Particles is VERY important and interesting. We glanced at 5.4, but not much work was done in it. Have a look at the Three different distributions though (Maxwell-Boltzmann, Fermi-Dirac, and Bose-Einstein) and try to interpret the equations physically using your knowledge of Identical Particles vs. distinguishable.

Ch 6, TIme Indie. Perturbation Theory

Get 6.1 and 6.2 down pretty good, have a look at the rest of the chapter for how the basic concept applies to the atom.

Ch 7, Variational Principle

7.1 and 7.2, (another important concept, not as interesting to me, but powerful tool nonetheless.)

 

[ytoruno]

pythagorean summed up a first course in quantum pretty well. I would only add the WKB approximation (ch 8) and general results about the hydrogen atom. I think however, that if you learn chapter 2 very well, you would be in good enough shape for a freshman; Start by learning the Hamiltonian operator and then solutions to the schrodinger equation for certain potentials.

 

[muppet]

For this particular project are the statistical distributions likely to feature highly on his reading list? They're obviously extremely important... but if you're just trying to "get by" for calculating wavefunctions I'd suggest all you really need to understand in this regard is Pauli exclusion and the Aufbau principle. The more pressing concerns of the basics (what QM means, the uncertainty principle, working through some solutions to the Schroedinger eqn, and the unfortunate fact that in a 3D coulombic potential the solutions are rather messier than that for a 1D "particle in a box") I'd say were plenty to be getting on with!

 

[Dahaka14]

ok, I'm on my way in griffiths, but i just spoke with my advisor, and he said to use liboff introductory qm, which should i use? he said my project will be in photo-ionization