, so time depend. of e-states is 
My crib sheet. (Please bring your Clebsch-Gordon tables as well)
First, some constants:
Time ind. Schrod. eqn is 
Time dep. Schrodinger equation is , so time depend. of e-states is
The expansion theorem says that if 
, then 
, and 
is the probability of finding state 
in the particular eigenstate 
.
The harmonic oscillator raising and lowering operators are 
. (Recall, 
)
Pauli spin matrices: 
, (All have the same eigenvalues, 
)
The eigenvectors of 
are 
. The eigenvectors of 
are 
Handy trig identities: 
Total angular momentum J=L+S.
Notation for eigenfunctions of angular momentum: 
The Hamiltonian for a particle in a magnetic field B is 
,
where the magnetic moment due to intrinsic spin is given by 
First order non-degenerate TIPT says the shift in energy of a state 
due to the addition of a perturbation 
is given by 
.
The variational theorem says 
, for any state 
you choose.
Time-Dep't PT: If H'(t) is added, starting at t=0, to a system initially in state N, the prob of making a transition to state m after time t is given by the absolute square of
.
The spontaneous rate of single photon decay is 
The lifetime of a state m due to spontaneous decays is 