Flashcards
QM2 Midterm Key Formulas
Cards in this deck (12)
- 1Time-independent non-degenerate perturbation theory: Energy through second order and state through first orderThe bottom line is only the CORRECTION term to the state (still need 0 order)
- 2Degenerate perturbation theory: Energy through second order and state through first orderWhere tilde (~) denotes diagonalized exactly in the degenerate subspace. (See typed notes on degenerate PT.) Sum does not connect states in degenerate subspace.
- 3Variational methodA method for approximating ground state energy and eigenfunction.
1. Guess a "trial" wavefunction that depends on one or more parameters
2. Find expectation value of energy of trial wavefunction ()
3. Minimize this energy value by varying the parameter(s)
The true ground state energy can never be higher than the lowest energy you get this way. The lower the energy you get, the more closely your trial wavefunction resembles the true ground state wavefunction.
This works because any conceivable trial wavefunction can be expressed as a superposition of true energy eigenfunctions.
This method can also work on, for instance, a first excited state, as long as you can construct your trial wavefunction so that it is orthogonal to the true ground state energy. (Otherwise, in minimizing your energy, you can slip past the first excited state and into a state that is mostly the ground state.) - 4Time-dependent perturbation theory: transition probability amplitude through first order
- 5Special cases of time-dependent perturbation theory: transition probabilityby harmonic I mean exp(-iwt) time dependence
- 6Dyson series (Higher order time-dependent perturbation theory)
- 7Fermi's Golden Rule: transition rateDerived from first-order time-dependent perturbation theory. Here harmonic means cos(wt) time dependence
- 8Einstein relationA is spontaneous,
B is absorption/stimulated.
A: 1/time. B: 1/(time*intensity)
- 9Electromagnetic radiation normalization
- 10photon emission/absorption GammaDerived from substituting the electromagnetic Hamiltonian into the Golden Rule.
- 11Electromagnetic Hamiltonian
- 12Definition of cross sectionEnergy absorbed or emitted per time
----------------------divided by----------------------
Energy per area per time
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- Physics Flashcards on QM2 Midterm Key Formulas, created by Yorick Andeweg on 03/03/2022.
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- Yorick Andeweg
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