Here were some Chapter by Chapter content learning goals SJP posted for students
before midterms:
Chapter 1:
Statistical interpretation
: this is our introduction to what "Ψ" tells you: you should
know how to use it to figure out probability of measurement. Do you know the difference
between probability and probability density? Can you compute expectation values or
standard deviations, given information about either discrete or continuous probabilities?
Operators
: You should be able to interpret and calculate expectation values of any
(position space) operator using the positionspace wave function "ψ(x)". Specifically, you
should know the "operator form" of momentum (p = ħ/i d/dx) You should know the
connection <p> = m d<x>/dt, and be able to work through calculations like the one
proving "conservation of normalization" using the Schrödinger equation.
Heisenberg relations
: You should have a preliminary sense of the uncertainty principle
(be able to state it, and physically interpret the two "sigma" terms, as well as calculating
them given a state)
We spent some time talking about the Postulates of quantum mechanics, the motivation
for the Schrödinger equation (including deBroglie's very important idea, the p = ħ /λ or p
= ħ k story), and a little history  you should be familiar with these.
_______________________
Chapter 2:
Schrödinger Equation:
The relation between the time DEpendent Schrödinger equation,
and the time INdependent SE is quite central here  you should know the "separation of
variables" trick, and thus be able to go from u
n
(stationary states,
i.e.
, solutions of H u =
Eu, the TISE) to more general states (with proper time dependence.)
Stationary States and Expectation Values:
You should have a clear idea of our
definition of "stationary state", how you find one (at least, for the specific examples of
infinite square well and harmonic oscillator), what they "look like" (graphs), what their
time dependence is, and be able to compute (and qualitatively explain or predict) what
expectation values look like (<x>, <p>, <H>, <x
2
>,
etc.
)
Expansion in Stationary States:
You should also understand how a more GENERAL
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 Fall '08
 STEVEPOLLOCK
 expectation values, time dependence

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