level: Level 1
Questions and Answers List
level questions: Level 1
| Question | Answer |
|---|---|
| Selection Rules | <n'l'm'|z|nlm>= 0 unless m'=m <n'l'm'|x or y|nlm> =0 if m' != m +- 1 <<n'l'm'|r|nlm> = 0 if l' != l +- 1 |
| Pertubation theory up until 1st Order energy correction to Hamiltonian | E'n = En + <Φ|H'|Φ> |
| Rayleigh Ritz Variation | <Φ|H|Φ>/<Φ|Φ> >= E0 |
| Can two particles be in the same single-particle state φ(r)? | Distinguishable particles - yes, bosons - yes, fermions - no (Pauli's exclusion principle) |
| For two identical particles that do not interact with each other, what are the many-body wave functions that satisfy the correct symmetry | Bosons : Φ(r,r') proprtional to Φ1(r) Φ2(r') + Φ2(r) Φ1(r') Fermions : Φ(r,r') proprtional to Φ1(r)Φ2(r) - Φ2(r) Φ1(r') Distinguishable particles : Φ(r,r') = Φ1(r) Φ2(r') |
| Hamiltonian of a particle in an e field | -∇H = qE |
| Pauli Spin matrices | in x: opposite of identity matrix in y: -i in position (2,1) , i in position (1,2) in z: identity matrix but bottom right is -1 |
| Relationship between potential A and B field | B is the curl of A A is not unique for a value of B, as you can add any scalar field to A and B is the same |
| Hamiltonian of a charged particle in a mag field B | H = (p-qA)^2/2m |
| Hamiltonian (very very basic definition) | H = T + V, where T is kinetic E and V is potential energy |