PH401 Quantum Physics 2000
About the 3rd 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 third exam:

3D simple harmonic oscillator

separable Schroedinger eqn

energy levels, quantum numbers, degeneracy (both ways)

commutators of 3D position &momentum

compatible observables

angular momentum

radial and angular momentum in terms of position & momentum

TISE in terms of radial and angular momentum

separable if simultaneous eigenstate of L_{z}, L^{2}, and
H

eigenvalues, quantum numbers

restrictions on quantum numbers

commutator of angular mom components

L_{+} &L_{} (not observable, not Hermitian)

matrix representation

Hydrogen atom

V(r)

TISE, radial part

steps to sol'n

terms in polynomial for given l and n

energy levels, n=1, 2, 3, 4...

l<n

Spin

angular momentum (but no angle)

quantum number, s, can be halfinteger

elementary particles are in eigenstate of S^{2} (ex electron has
s=1/2)

m_{s}

If s is halfinteger, obeys exclusion principle

eigenstates and averages

energy levels not only dependent on n

If there's more than one e, shielding makes lower lstates lowere in energy.

Nucleus "oribiting" electron creates a magnetic field, and an interaction
potential proportional to L^{.}S

with L^{.}S in hamiltonian, m_{l }& m_{s} no
longer good quantum numbers

Angular momentum addition

vector addition

limits on J give limits on j

m_{j} ranges from j to j (like m_{l} and m_{s})

Spherical coordinates and wavefunctions

d^{3}r=r^{2}drsin^{2}qdqdf

probability of being within dr of r

parity, x>x, y>y, z>z; OR r>r, q>pq,
f>p+f

parity of angular mom state is (1)^{l}