Chemistry 354L: Physical Chemistry 11, Fall 2006 Oct. 6, 2006
Exam #1
Name
UT EID
Note that the problems are of different length, and different levels of difficulty. Also each is
worth a different number of points (Total=100).
Scores: #1
#2
#3
Misc
Position of a particle in a box
x Expectation value of the position operator
x = * ( x ) x ( x ) dx
For a particle in a box in the ground state
2
x
x
x = sin x sin dx
L
L0 L
L
x 2 x sin ( 2 ax ) cos ( 2 ax )
x sin ( ax ) dx = 4 4 a 8a 2
L sin ( 2
Chemistry 354L: Physical Chemistry II, Fall 2006
Name
UT EID
Nov. 3, 2006
Exam #2
Note that the problems are of different length and levels of difculty. Also each is worth a
different number of points (Total=100).
Scores: #1
#2
#3
Miscellaneous
CH354L Physical Chemistry II, Fall 2016
Quantum Mechanics, Molecular Structure, & Spectroscopy
Problem Set 3: Wavefunctions & Operator Algebra
1) In class, we discussed the mathematical properties that a wavefunction of a system must
obey. Use that inform
CH354L Physical Chemistry II, Fall 2016
Quantum Mechanics, Molecular Structure, & Spectroscopy
Problem Set 1: Quantized Behavior
1) The fundamental equation of quantum mechanics is the Schrdinger equation. For many
systems, well find that solutions to thi
CH354L Physical Chemistry II, Fall 2016
Quantum Mechanics, Molecular Structure, & Spectroscopy
Problem Set 4: Wavefunctions & Operator Algebra
1) In class, we have encountered a few problems now were weve qualitatively described what
happens to the wavefu
Physical Chemistry II Course Notes
Graeme Henkelman October 7, 2006
Course Overview
These notes contain an outline of the topics covered in the physical chemistry II course. We will not cover all the material in the textbook, so here I will briey d
CH354L Physical Chemistry II, Fall 2016
Quantum Mechanics, Molecular Structure, & Spectroscopy
Problem Set 2: The Schrdinger Equation and One Dimensional Potentials
1) Consider a particle moving through space with a fixed amount of energy E. This particle
Point Scheme:
#1: 18 pts.
#2: 16 pts.
#3: 16 pts.
#4: 14 pts.
#5: 16 pts.
#6: 20 pts.
The wave function has units of (Length )^(-Nn/2) where "n" is the dimensionality and "N" is
the number of particles. So, the 1-D wave function of 1 electron has units (L
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1: Poker odds
A: Three of a kind
Accepted solution #1
Total poker hands: Choose 5 cards from 52 total -> 52C5
In[67]:=
Out[67]=
52
5
N 52
2.59896
5
47
106
First card can be any from one suit: Choose 1 cards from 13 ranksl -> 13C1
In[69]:=
Out[69]=
13
1
N
Hydrogenatom:Interac0onofaposi0velychargedpar0cle
(proton)withanega0velychargedpar0cle(electron)
2
e
V (r ) =
4 0 r
p
r
Ifweassumethattheproton(muchheavierbyaboutafactorof2000)isat
restwhiletheelectronismobile,wecanwriteapproximatehamiltonianfor
theenerg
The solu)on for electrons and proton
will be done in steps
1.
(
)
(
)(
H e re ; rp1 , rp1 = Ee rp1 , rp 2 re ; rp1 , rp1
)
We have done that
2.
(
H p p rp1 , rp2
)
2
e2
2
2
=
p1 + p 2 +
+ Ee rp1 , rp 2
4 0 R12
2mp
(
)
(
) ( r
p
p
DiatomicmoleculesFromLi2toF2
Moleculargroundandexcitedstateorbitalfromatomicorbitals
g = ( 2 + 2 SAB )
( A + B )
1/ 2
u = ( 2 2 SAB ) ( A B )
1/ 2
u
A
B
g
Thesimplestdiatomics
Electron
No.bonding Equilibriumdistance Dissocia.on
congura.ons an.bonding
en
5
Harmonic Oscillator
The harmonic potential is a good description for many interactions in chemistry, including chemical bonds. Low energy vibrational motion, for example, can be accurately described as a harmonic oscillator.
5.1
Classical Harmo
6
Rotational Motion
So far we have used quantum mechanics to describe translation and vibration. In this nal section on quantum mechanics, we will consider rotational motion. Our strategy will be to use the separation of variables technique to sepa
7
Statistical Mechanics
Statistical mechanics is the study of how macroscopic properties can be derived in terms of detailed microscopic properties. For chemists, statistical mechanics involves understand the macroscopic laws of thermodynamics in t
3
Bound States
The Schrdinger equation is a second order dierential equation because it contains o the second derivative of the wavefunction. For a second order equation, the solutions have two degrees of freedom. In the case of a free particle, th
4
Time dependence
So far, we have used the time-independent Schrdinger equation to nd stationary o states. These stationary states do not change with time. We can see this by looking at the time-dependent Schrdinger equation o (r, t) (4.1) 2m t wh
2
Fundamentals of quantum mechanics
In the last section, we described the experimental motivations for a new type of physics at the atomic scale; one that captures the observed wave-like properties of elementary particles. Arguably the most intuiti
Midterm1Key
1) (20pts)
(a)(b)(8pts)
d 2 f (x)
= ! f (x)
dx 2
f (x)
df ( x )
dx
e! x
! e! x
!" x
!" e
! cos(! x )
!" x
e
sin(! x )
cos(! x )
e ! x [1pt], e!
equation.
d 2 f (x)
dx 2
! 2 e! x [1pt]
!" sin(" x )
"x
2 "! x
! e [1pt]
!" sin(" x ) [1pt