Paul Avery
PHY3101
Fall 2015
Name (PRINT):
Bonus Problem 5
Due Monday, Oct. 19, 2015
For all problems
(1) Put your name clearly in the printout or file
(2) Describe what software you used
(3) Show the program, including a screenshot or printout. Make sure it is readable with large
fonts and good contrast. I can’t grade it if I can’t easily read the screenshot.
1. (5 pts) A set of polynomials Qn ( x ) is generated from the formula
Qn ( x ) = ( −1) e x
n
2
d n ⎛ − x2 ⎞
e
⎠
dx n ⎝
Print out the polynomials Q0 through Q10 in factored form.
2. The functions ψ n ( x ) = AnQn ( ax ) e−a
2 2
x /2
are solutions of the Schrödinger equation for the
(
)
potential p̂ 2 / 2m + 12 mω 2 x 2 with energy En = ω n + 12 . An is a normalization constant.
a. (5 pts) Find a. You can do this by plugging the n = 0 solution into the SE.
b. (5 pts) Find the normalization constant An for n = 0 through 5
1