ps8 - Harvard University Physics 143b: Quantum Mechanics II...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Harvard University Physics 143b: Quantum Mechanics II Problem Set 8 due Friday November 19 1. Consider non-relativisitic electrons constrained to move on a thin ring of radius R . Assuming we can ignore motion except along the angular direction of the ring, which is labelled by an angle , the Schrodinger equation for the wavefunction ( ) is- h 2 2 mR 2 d 2 d 2 = E. (1) The eigenfunctions are = e i / 2 , and the eigenenergies are h 2 2 / (2 mR 2 ), where is any integer. Now magnetic flux is inserted in the center of the ring. (a) The vector potential can be chosen to have only an angular component. Show that A = / (2 R ), and so the Schr odinger equation is modified to 1 2 mR 2 h i d d- q 2 ! 2 = E (2) where q is the charge of the electron. (b) List the eigenvalues of (2). (c) Plot the total ground state energy of 5 electrons as a function of (ignore electron spin, and you can use Mathematica if you wish)....
View Full Document

This note was uploaded on 02/15/2011 for the course PHYS 143B taught by Professor Unknow during the Spring '10 term at Harvard.

Page1 / 2

ps8 - Harvard University Physics 143b: Quantum Mechanics II...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online