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 s
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 f
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 displacem
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 separat
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
F
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 the
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
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
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: Nor
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