Physics
410
Quantum Mechanics Fall 2010
Homework
#4 Sept
24, 2010
due
Friday, Oct 1, 2009
Griffiths
problems 2.11 (a)-(b), 2.12, 2.16
Johnson
4.1 In Example 2.4, Griffiths shows how to
use the raising operator a+
to get the first excited harmonic oscillator state, y1(x) from the ground state
wfn y0(x). Apply again to get the second excited
state, y2(x) (do not worry about
overall normalization). Does this agree with what we find in section 2.3.2?
Johnson
4.2: In the
following, do not evaluate any integrals.
Instead, I want you to practice your dimensional thinking.
Consider
from -´ to ´.
(a)
Up to some dimensionless constant, what do you expect for the normalization A?
(b)
Up to some dimensionless constant, what do you expect for < x >?
(c)
Up to some dimensionless constant, what do you expect for < x2 >?
(d)
Up to some dimensionless constant, what do you expect for < p >?
(e)
Up to some dimensionless constant, what do you expect for < p2 >?
(f)
Do you expect this wavefunction to satisfy the Heisenberg uncertainty
principle? Why or why not?
(g)
Extra credit: Are any of the above integrals "easy" to evaluate,
without using a table of integrals or a computer program of any sort? If so, do
so.