Name:
Chem 3322 test #1 out of 40 marks, given on Feb. 14, 2014
I want complete, detailed answers to the questions. Show all your work to get full credit.
Data:
The Schrdinger time dependent equation
Problem 1 20 marks
For the harmonic oscillator with potential energy V(:c) = kx2/2 = mw2x2/2) we showed
that the (unnormalized) ground state wavefunction is 1/)(Lr) = 6"2
with or : mw/Zh.
a) 10 marks
Chem 3322 homework #2 solutions, out of 17 marks
Problem 1 10 marks
Suppose we have a wavefunction
(x, t) = 1 (x)eiE1 t/ + 2 (x)eiE2 t/
(1)
with E1 = E2 . Write down an expression for the probability
Chem 3322 homework #2 solutions out of 32 marks Problem 1 4 marks Consider the operator d d ^ A=x - x dx dx (1)
What does this operator do to a function f (x)? Based on your answer, express this opera
Chem 3322 homework #3 due Feb. 6, 2015
Problem 1 particle in a box
Consider a particle in a one-dimensional box of length L in its lowest energy (ground)
stationary state. Calculate the probability th
Chem 3322 homework #7 due April 10, 2015
Problem 1 Rigid Rotor / Harmonic Oscillator
The spacing between vibrational energy levels is substantially larger than the spacing
between (low-lying) rotation
Name:
Chem 3322 test #1 out of 40 marks, given on Feb. 14, 2014
I want complete, detailed answers to the questions. Show all your work to get full credit.
Data:
The Schrdinger time dependent equation
Chem 3322 homework #6 due March 13, 2015
Problem 1 expectation values
For a particle in a 1d box, use the normalized wavefunctions derived in class to compute
a) x
b) x2
d) p2
x
c) px
(1)
for the grou
Name:
Chem 3322 test #1 solutions, out of 30 marks
I want complete, detailed answers to the questions. Show all your work to get full credit.
indenite integral :
sin2 (ax)dx =
x sin(2ax)
2
4a
(1)
The
Chem 3322 homework #7 out of 27 marks
Problem 1 9 marks
The spacing between vibrational energy levels is substantially larger than the spacing
between (low-lying) rotational energy levels, which itsel
Chem 3322 homework #9 solutions, out of 36 marks
Problem 1 5 marks
The vibrational frequency of I2 is 208 cm1 . At what temperature will the population in
the rst excited state be half of the ground s
Advantages of Raman: can use any photon
wavelength you want. If you use visible light:
1. can avoid absorption of light by H2O, CO2, etc.
2. can use optical microscopy to focus with a
spatial resoluti
l raw : MU
as 4;.m;ww/
\
Mg m m W; J
v5 Mu t W :L p LC,de " ax, ML
MO M to M tLL Tr: '1
Q UL TC - Mm; , txuM MIA» 1 1" (Vi a
null wawax (IWISVMAQ E-
,
F
\« A: 3 Fwy
r»
L),
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u
o<i
t . 6 Z
Anharmonicity
In real molecules, highly sensitive vibrational
spectroscopy can detect overtones, which are
transitions originating from the n = 0 state for
which n = +2, +3,
Overtones are due to anha
Particle in a box : Quantum Dots
The color of light emitted by a semiconductor material
is determined by the width of the energy gap
separating the conduction and valence energy bands.
In bulk semicon
Chem 3322 homework #3 solutions, out of 37 marks
Problem 1 9 marks
Consider a particle in a one-dimensional box of length L in its lowest energy (ground)
stationary state. Calculate the probability th
Chem 3322 homework #3 solutions, out of 10 marks
Problem 1 5 marks
The electrons in benzene can be approximated as particles on a ring. Calculate the
diameter of this electron ring if it is assumed th
Chem 3322 homework #2 due Jan. 29, 2016
Problem 1 10 marks
Classical physics predicts that there is no stable orbit for an electron moving around a
proton. What criterion did Niels Bohr and/or Louis d
Chem 3322 homework #1 solutions, out of 34 marks
Problem 1 16 marks
a 4 marks) Show that u(x, t) = sin(kx t) satises the classical wave equation by
directly using the function sin(kx t) in the wave eq
Chem 3322 homework #5 solutions, out of 10 marks
Problem 1 10 marks
a 3 marks)
Consider two particles of masses m1 and m2 in one dimension, interacting through a
potential that depends only upon their
Chem 3322 homework #8 due April 17, 2015
Problem 1 Vibrational Energy Levels
Relative to the n = 0 vibrational level of the ground (X) electron state of
79
Br2 , the
vibrational levels (n) of the exci
Chem 3322 homework #8 solutions, out of 15 marks
Problem 1 15 marks
Relative to the n = 0 vibrational level of the ground (X) electron state of
79
Br2 , the
vibrational levels (n) of the excited (B) s
Chem 3322 homework #9 due April 24, 2015
Problem 1
The vibrational frequency of I2 is 208 cm1 . At what temperature will the population in
the rst excited state be half of the ground state?
Problem 2