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Foundations of Physics 3A


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Rhianna Moore


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[Front]


Selection Rules
[Back]


<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

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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
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 (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
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)
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