PH401 Quantum Physics 2000
About the 2nd exam:
The exam will contain 10 multiple choice questions, and 6 problems requiring
calculation, explanation, and/or derivation. You may use a calculator and
one 5"X7" card of handwritten equations.
Topics to review for second exam:

wavefunction is position rep, y(x)=<xa>

momentum amplitude is momentum rep, f(p)=<pa>

energy amplitude is energy rep, a_{n}=<na>

inner product, probability, norm

expectation values

state vectors and operators as matrices

changing basis

operator diagonal in own basis

COMPLETE ORTHONORMAL SET OF BASIS VECTORS

normalized

orthogonal

completeness and the unit operator

the set of all eigenvectors of ANY observable is complete

SIMPLE HARMONIC OSCILLATOR

TISE in vector/operator form

HAMILTONIAN

raising and lower operators

COMMUTATORS

[x,p], [a,a^{+}], [H,a], [H,a^{+}]

Show an> and a^{+}n> are energy eigenstates

energy levels

a^{+}an> = n n>

finding expectation values and uncertainties <x>, Dx,
<p>, Dp

Time dependent Schroedinger eqn in vector/operator form

y(t)>

d<Q>/dt

Conservation Laws