Solutions No-fault QUIZ 3
Fri. Nov. 30, 2012
1) Determine the possible spin-states = |S MS (S = s1 + s2 ) for positronium i.e., a
bound electron-positon pair. Determine the values s1 s2 for each state.
S = |1/2 + 1/2| = 1 or 1/2 1
No fault QUIZ 2
Wed. Oct. 31, 2012
1) The dimensionless destruction operator for the harmonic oscillator (sometimes called
a ) is dened by a = (Q + iP )/ 2, where P = id/dQ. Determine the Hermitian
conjugate of a, and show that expectation val
Solution QUIZ 1
Wed. Oct. 3, 2012
Answer all parts. For each part give an appropriate formula and when appropriate a
numerical answer (1 signicant digit suces).
1) An electron of energy E = 1.9 eV has a de Broglie wavelength of about 0.9 nm. W
NOTE $0 have
Sejf = PSef .1
,' xoeg a 6/2
bmmded MW, Val, a > O
3; recall: pr3 z? V4001:
$de wool = 1
:a) Z!(><I)'r-= , 61:: [3 Pure/(,7
> mm; = mo)?
I Z ~21x~XOi/a
I W = A e
a P hat
Solutions 2nd Midterm Exam Phys 324A
1. [40 pts] - Formalism of Quantum Mechanics
a) (10 pts) Evaluate the fundamental commutator of quantum mechanics [x, p], where p
is the momentum operator, and explain using the generalized uncertainty principle the
Name _Student ID _ Score_
For each of the questions below, show all work and explain the steps you used to arrive at your answer.
A (classical) ball moves back and forth in a track with steep sides.
The track consists of two