MATH 164, Spring 2001 Due Date: Name(s):
Honors Project 13: Vibration in Molecules
The simplest approximate description of vibration in molecules involves functions whose form is dictated
by the laws of quantum mechanics to be
n(z) = hn(z)e-z2
/2
, n = 0, 1, 2, . . .
where
h0(z) = 1, h1(z) = 2z, h2 = 4z2
- 2,
and, more generally,
hn(z) = (-1)n dn
dzn
e-z2
.
Problems
1. Generate h3(z), h4(z), and h5(z).
2. The laws of quantum mechanics applied to this description of vibration tell us that for all integers n,
z2
n -
d2
dz2
n =
En
E0
n
where En is an energy associated with the nth wavefunction. Find En/E0 for n = 1, 2.
Contributor: Dr. Clifford Dykstra
Department of Chemistry, IUPUI