Chemistry 482: Physical Chemistry 2
October 28, 2013, Quiz #4
Instructions: Write your name on this sheet of paper and staple it together with your solutions when
you are finished.
(1) (1point) (a) Tr
Towards Atomic Electronic Structure
Particle on a Ring
Particle on a Sphere
Uses particle on a ring
as a starting point: the
sphere is a stack of rings
Particle on a sphere Hamiltonian also applies
to
Towards Atomic Electronic Structure
Particle on a Ring
Particle on a Sphere
Uses particle on a ring
as a starting point: the
sphere is a stack of rings
The Hydrogen Atom
Uses particle on a sphere
as a
Ch11. Quantum States of Many-Electron Atoms
Many-electron spin and orbital angular momentum operators are given by
sums of single electron operators
L lj
j
S sj
j
For the z components we have
Lz ljz
j
Example: Evaluate the following eigenvalue equation for a wave function of the
electron configuration 2p13p1
1 2 p 1 3 p 2 2 p 2 3 p 1 1 2
L2
1
1
1
1
2
1
?
2 p1 1 3 p1 2 2 p1 2 3 p1 1 1 2
2
Exam
Realistic Numbers for HeH+ Molecule
a=He
72.1 36.7
H eV
36.7 47.1
1.00 0.45
S
0.45 1.00
b=H
d c c 2ca cb Sab
2
2
a
2
b
86%
He
2%
H
12%
Roots of the secular determinant are found using
H aa
H
Ch12. Chemical Bonds in Diatomic Molecules
The Hamiltonian of H2+ sums on the kinetic energies of each particle. The
potential energy terms account for all pair-wise Coulombic interactions.
e2 1 1
e2
Ch12. Chemical Bonds in Diatomic Molecules
The Hamiltonian of H2+ sums on the kinetic energies of each particle. The
potential energy terms account for all pair-wise Coulombic interactions.
e2 1 1
e2
Chemistry 482: Physical Chemistry 2
September 11, 2013, Quiz #1
Instructions: Write your name on this piece of paper and staple it together with your solutions when
you are finished. Show your work on
Chemistry 482: Physical Chemistry 2
November 11, 2013, Quiz #5
Instructions: Write your name on this sheet of paper and staple it together with your solutions when
you are finished.
(1) (1point) (a) T
Chemistry 482: Physical Chemistry 2
October 9, 2013, Quiz #2
Instructions: Write your name on this sheet of paper and staple it together with your solutions when
you are finished.
(1) (1point) (a) Tru
Chemistry 482: Physical Chemistry 2
September 25, 2013, Quiz #2
Instructions: Write your name on this sheet of paper and staple it together with your solutions when
you are finished.
(1) (1point) (a)
Vibrational Quantum States in Polyatomic Molecules
Key Idea: Vibrations delocalize onto bond stretching and bending
motions with similar intrinsic frequencies
How to Treat Interesting Systems With Ham
Ch10. Helium: The Smallest Many-Electron Atom
The Schrdinger equation cannot be solved analytically for atoms possessing
more than one electron. Approximations must be introduced.
The Hamiltonian sums
Ch3. Quantum Mechanical Postulates
Postulate 1
The state of a quantum mechanical system is completely specified
by its wave function. The probability that a particle will be found at
time t0 in a spat
Ch4. Quantum Mechanics on Simple Systems
In chapter 2, we obtained the Schrdinger equation for stationary states
d 2 x
V x x E x
2
2m dx
2
Eq. 4.3
Lets first treat a system in which the potential e
Mathematical Arguments are the Foundation of
Quantum Mechanics
Chapter 2 argues for the plausibility that the Schrodinger equation
describes wave-particles
Chapter 3 presents the postulates (i.e. assu
Quantum Mechanics Arose Out of the Interplay Between
Experiments and Theory
Early in the 20th century, a number of experiments found that the
predictions of classical physics were inconsistent with o
Potential Energy
Tunneling Through a Potential Energy Barrier
V0
Zone I
V(x)=0
Zone II
V(x)=V0
0
Zone III
V(x)=0
L
The goal of this problem will be
to obtain the probability that a
particle approachin
Ch6. Commutation Relations
Two observables can be known simultaneously only if the outcomes of the
measurements are independent of the order in which they are conducted.
Mathematically, this means tha
Ch7. Harmonic Oscillator
Write the Hamiltonian and expand the potential energy in a Taylor series
p2
H
V x
2m
2
2
p V dV x 1 d V x 2
H
0
2m
2 dx 2 0
dx 0
(1)The constant leading term, V0, is droppe
Hierarchy of Systems in Quantum Mechanics
1.
Simple systems with analytic solutions to SE
Particle in box
One-dimensional harmonic oscillator
Particle on sphere
Hydrogen atom
2. Interacting systems wi