Foundations of Physics 3A
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Foundations of Physics 3A - Leaderboard
Foundations of Physics 3A - Details
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| 🇬🇧 | 🇬🇧 |
| 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') |
| 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 |
| Parity and angular momentum in even-even nuclei | Parity = +1, as for every nucleon we can find another with the same parity Angular momentum = 0, as nucleons will pair up and give no net total |
| What are magic numbers | Atomic numbers that correspond to completely filled shells, that make elements much more stable (meaning more stable isotopes). These numbers are 2, 8, 20, 28, 50, 82, and 126. |
| Difference between mean lifetime and half life | Practically, a factor of ln(2). Mean lifetime - average time to decay, also the time taken for a sample to decrease by 0.368. Half life - time for half of sample to deay |
| Parity and angular momentum of an even-odd nucleus | (L +/- 1/2)^L |
| Selection rules | |J_p - J_d | <= l <= J_p + J_d and (-1)^l = +/- P_d*P-P for an E/M l transition |
| Strength of forces (strong to weak) | Strong - EM - Weak - Gravity |
| How does coupling constant effect strength of a force | Higher coupling constant = stronger force |
| Color in hadrons | Attractive force only exists when it is colourless, so for mesons you have a quark and an antiquark, and then for baryons you have one of each colour (mixing 3 colours gets white) |
| What must be conserved at each vertex of a Feynmann diagram | Charge, baryon number and lepton number |
| Forbidden interactions | - Something decaying into a quark and lepton (stuff will not be conserved) - Photon decaying into photons, as there is no charge for a photon - Gluons can't decay into a gluon and another force mediator, because colour rules violate it |
| Quark Decays | T -> b -> c -> s -> u <-> d |
| Wavefunction properties to remember | For fermions, total wavefunction is antisymmetric For ground state spacial wfn is symmetric Colour wavefunction is antisymmetric |