Physics 512
Winter 2003 Final 4:007:00 (3 hours), April 23, 2003 Solutions
[30 pts] 1. A particle of mass m and charge q sits in an isotropic three-dimensional harmonic oscillator potential, and is described by the Hamiltonian H0 = p2 1 + m 2 r 2 2m 2
Not
Physics 512 Homework Set #12 Solutions
Winter 2003
1. The differential cross section for the ejection of an electron with momentum kf by an incident photon of momentum k ( = c|k |) and polarization ^ (the photoelectric effect) may be written as d |kf | 3
Physics 512 Homework Set #11 Due Friday, April 4
Winter 2003
1. This is similar to Sakurai, Chapter 6, Problem 7. Two identical spin- 1 fermions are 2 placed in a one-dimensional infinite square well of size L V (x) = , x < 0 or x > L; 0, 0 < x < L
We ass
Physics 512 Homework Set #10 Solutions
Winter 2003
1. This is based on Sakurai, Chapter 5, Problem 28. A hydrogen atom is initially in its ground state (1s). At time t = 0 we turn on a spatially uniform electric field as follows: 0 t<0 E(t) = E0 e-t/ z t
Physics 512 Homework Set #9 Solutions
Winter 2003
Note: The homework set posted on the web had a second page (part c) of problem #3 and problem #4). I mistakenly omitted the second page on the set I handed out in class, so only the rst three problems are
Physics 512 Homework Set #8 Solutions
Winter 2003
1. This is based on Sakurai, Chapter 7, Problem 9. Consider scattering by a repulsive -shell potential 2mV (r) = (r a), >0 h2 a) Set up an equation that determines the s-wave phase shift, 0 , as a function
Physics 512 Homework Set #7 Solutions
Winter 2003
1. Consider the scattering of a beam of spinless particles of momentum hk initially traveling along the + direction by a potential of the form z V (r ) = V0 (x)(y b)(z) + (x)(y + b)(z) a) Calculate the sca
Physics 512 Homework Set #6 Due Monday, March 3
Winter 2003
1. One dimensional scattering. Consider scattering from a potential V (x) = -g(x). If we send in a particle from the left inc (x) = eikx x<0
there will be an amplitude for both reflection and tra
Physics 512 Homework Set #5 Solutions
Winter 2003
1. This problem is essentially Merzbacher, Chapter 18, Problem 4 [or Sakurai, Chapter 5, Problem 1]. Consider a one-dimensional harmonic oscillator perturbed by a constant force 1 p2 + m 2 x2 - F x H= 2m 2
Physics 512 Homework Set #4 Solutions
Winter 2003
1. A molecule is composed of six identical atoms which form a regular hexagon. Consider a single electron which can be localized on any one of the atoms. Let |n denote the state in which it is localized on
Physics 512 Homework Set #3 Solutions
Winter 2003
1. Let Sq1 1 and Tq2 2 be two irreducible spherical tensor operators of ranks k1 and k2 , (k) respectively. We may form the tensor product Wq defined by
(k) Wq = (k (k k1 k2 ; q1 q2 |k1 k2 ; k q Sq1 1 ) Tq
Physics 512 Homework Set #2 Solutions
Winter 2003
1. We may add three angular momenta, J1 , J2 and J3 , by rst adding the rst two, J12 = J1 + J2 , and then by adding this result to the last one, J123 = J12 + J3 . Using this (or any other suitable method),
Physics 512 Homework Set #1 Solutions 1. The Pauli Hamiltonian (for gs = 2) was presented as H= 1 q q S B + q (p A )2 2m c mc
Winter 2003
Using the properties of the Pauli matrices (and being careful with operators), show that this may be rewritten in the