Lecture 1 Notes: Perturbation Theory
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 determine the state o
Lecture 6 Notes: Classical Velocity Target
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
Lecture 5 Notes: Harmonic Oscillator
Last time
Classical Mechanical Harmonic Oscillator
1
* V(x) kx2 (leading term in power series expansion of most V(x) potential energy 2
functions)
* x is displacement from equilibrium (x = 0 at equilibrium)
* angular f
Lecture 2 Notes: Normal Modes
2u12u
1-D Wave equation
x2 v2 t2
* u(x,t): displacements as function of x,t
* 2nd-order: solution is sum of 2 linearly independent functions
* general solution by separation of variables
* boundary conditions give specific ph
Lecture 8 Notes: Wave-Packets PIB
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)| moves onl
Lecture 9 Notes: Infinite Expectation Values
Postulates, in the same order as in McQuarrie.
1.
2.
3.
(r,t) is the state function: it tells us everything we are allowed to know
For every observable there corresponds a linear, Hermitian Quantum
Mechanical o
Lecture 7 Notes: Ordinary Time Equations
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 3 Notes: Mechanical Particle
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 uncerta
Lecture 4 Notes: Quantum Mechanics
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. What do w
Lecture 10 Notes: Self-Consistent Fields
In the previous lecture, we covered all the ingredients necessary to choose a
good atomic orbital basis set. In the present lecture, we will discuss the
other half of accurate electronic structure calculations: how