Homework 6. Due Mon Nov 12 at 5pm in Prof. Ginger’s mailbox.
CIRCLE YOUR ANSWERS AND KEY INTERMEDIATE RESULTS
USE MAPLE WHENEVER POSSIBLE
STAPLE YOUR PAPERS TOGETHER
INCLUDE ALL COMPUTER PRINTOUTS (with commentary)
Levine Problems:
8.1 – Hydrogen variation. If you’re clever you might not have to do any math, but must
explain fully.
8.12– What went wrong?
8.42-Normalized eigenvalues and eigenvectors of a matrix
Additional Problems:
Understanding Selection Rules
1) Derive the selection rules for the particle in a 1D box by finding when the transition
dipole moment is nonzero. Create a Maple animation of the time evolution of the
electron probability density of an equal superposition of two states between which
transitions are allowed, and for two states between which transitions are forbidden.
Interpret the resulting motion. You may scale the equations to dimensionless quantities
for the plots. (This will be a VERY fast problem if you’ve been thorough in your
homework solutions up till now).
2) Complete the missing steps from lecture in the calculation of the radiative lifetime of
the 2p
0
state of a hydrogen atom.
2a) Calculate the transition dipole moment for 2p
0
to 1s.
2b) Calculate the Einstein A coefficient for this transition and the lifetime of the state.
2c) Check your answer in 2b) against the experimental values from the NIST reference
tables online at http://physics.nist.gov/PhysRefData/ASD/lines_form.html This is
nice—you’ve come far enough to actually calculate REAL values for things!
3) The particle-in-a-box wave functions form a complete set. Use an appropriate number
of them to create a linear variation function for the potential given in Levine 8.5 and find
upper limits for the ground and first 3 excited state energies, ensuring that your
calculation of the ground state energy is accurate within 0.0013% (note: the true energies
of the first 2 states are given in Levine 8.5 and 8.15). Make sure you use assume(L>0)
etc.
