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Homework 2 Part 2
(Due Feb 1
st
)
1.
You have seen that linear combinations of timeindependent orbitals can be combined via the
LCAO theory. We will now show that this also applies to timedependent wavefunctions.
Given that two wavefunctions,
g
m
and
g
n
, are orthonormal and stationary states with respect to
the timedependent Hamiltonian, show that
ΨG±, ²³ = ´
µ
g
µ
G±³¶
·¸¹
º
»/ℏ
+ ´
¼
g
¼
G±³¶
·¸¹
½
»/ℏ
satisfies the timedependent Schrodinger equation.
2.
Calculate the ΔE for a transition between the ν=0
b
ν=1 state, for a:
a.
Harmonic oscillator obeying Hooke’s law
b.
Morse Potential
3.
Determine the total degrees of freedom for each molecule below, as well its translational,
rotational, and vibrational degrees of freedom.
a.
C
6
H
6
b.
Formaldehyde
c.
CH
3
Cl
4.
Describe the normal modes of vibration of SO
2
and CS
2
. Which are Raman active and which are
infrared active?
5.
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This document was uploaded on 01/03/2012.
 Fall '09

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