Lecture 7 Notes: Time-Dependent Equations
Last time: TimeDependent Schrodinger Equation
H =i
H
t
Express in complete basis set of eigenfunctions of timeindependent H
H
cfw_n(x), En
(x, t) =
cj eiEjt/nj(x)
j
For 2-state s, we saw that
1. |*(x, t) (x, t)| m
Lecture 3 Notes: Free Particle Theory
Last time:
Build up to Schrdinger Equation: some wonderful surprises
* operators
* eigenvalue equations
H
H
* operators in quantum mechanics especially x x and px in x
* non-commutation of x and px : related to uncert
Lecture 5 Notes: Hermite Equation
Last time
Simplified Schrdinger equation: 1/2x, (k)1/2 n
2
2E
2
2
0
(dimensionless)
n
reduced to Hermite differential equation by factoring out asymptotic form of . The asymptotic
is valid as 2. The exact v is
Hermite p
Lecture 4 Notes: Quantum Mechanic Theory
Last time
What was surprising about Quantum Mechanics?
Free particle (almost exact reprise of 1D Wave Equation)
Can't be normalized to 1 over all space! Instead: Normalization to one particle between
x1 and x2. Wha
Lecture 2 Notes: Classical Chemistry Equations
Last time:
Two-slit experiment
2 paths to same point on screen
2 paths differ by n-constructive interference
1 photon interferes with itself
get 1 dot on screen-collapse of state of system to a single dot
to
Lecture 1 Notes: Introduction to Course
Lets begin:
Chalk demonstration.
Trajectory x(t), p(t): can predict end-point xend, pend, tend, after observation of short segmentof
trajectory at early t.
Decrease mass of thrower, chalk, and target by 100 without
Lecture 10 Notes: Perturbation Theory
What is Perturbation Theory good for?
1.
Computing the effects (pattern of energy levels, relative transition intensities in
a spectrum, intramolecular dynamics) of a distortion of the potential energy
function from a
Lecture 6 Notes: Dimensionless Variables
Last time:
1/2
x
h
xp
p h
a 21/2
2
O
1/2
1/2
xp 2
p 2
dimensionless variables
p
annihilation operator
ip xp
ip
a
1/2
1/2
i
xp
creation operator
a a
a a
h
x
n h 2 n/2
1/2
a
, x
a
2
1/2
h i
2
p
n
a
a
av v
a
Lecture 8 Notes: Integral Formulas
x
1/2
n
p n
a 2
a
t
2
p
2
1/2
ip
1/2
p
x
1/2
i
1/2
a a
a a
n
x
x
ip x
2
x
1/2
1/2
2
n
2
a
most important
1/2
i
p
a
a
a
avv1/2v1, e.g. a3vvv1v21/2v3
avv11/2v1, e.g. at10vv10v11/2v10
What is so great about a,a ?
Born
Lecture 9 Notes Valence States
So far we have seen several exactly soluble quantum mechanical problems.
1.
Particle in an infinite-wall box.
* useful insights into valence states of diatomic and conjugated polyatomic
molecules. The system size is related
Domingo Carmona
David Espinosa (latn American)
11/29/2016
Writing Assignment #2
Rafael Leonidas Trujillo Molina was an untouchable dictatorship who ruled the
Dominican Republic from February 1930 until his assassination in may 1961. 1 During his 31
years