Difference between revisions of "Forest FermiGoldenRule Notes"
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Fermi's Golden rule is used to calculate the probability (per unit time) of a quantum mechanical transition between two quantum states. Although Fermi first coined the term "Golden Rule", Dirac developed most of the machinery. | Fermi's Golden rule is used to calculate the probability (per unit time) of a quantum mechanical transition between two quantum states. Although Fermi first coined the term "Golden Rule", Dirac developed most of the machinery. | ||
| − | :<math>| M_{i,f}| ^2 = \int \psi_i^{*} H_{ | + | The first part of the Golden rule is the transition matrix element <math>M_{i,f}</math> |
| + | |||
| + | :<math>| M_{i,f}| ^2 = \int \psi_i^{*} H_{int} \psi_f dv</math> | ||
where | where | ||
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: <math>\psi_i</math> = initial quantum state of the system | : <math>\psi_i</math> = initial quantum state of the system | ||
: <math>\phi_f</math> = final quantum state of system after a transition | : <math>\phi_f</math> = final quantum state of system after a transition | ||
| − | : <math>H_{ | + | : <math>H_{int}</math> = the part of the total Hamiltonian (<math>H_{tot}</math>) which describes the interaction responsible for the transition. |
:<math>H_0</math> = Unperturbed ("steady state") Hamiltonian | :<math>H_0</math> = Unperturbed ("steady state") Hamiltonian | ||
| − | : <math>H_{tot} = H_0 + H_{ | + | : <math>H_{tot} = H_0 + H_{int}</math> = total Hamiltonian describing the quantum mechanical system |
: <math>dv</math> integration over all space | : <math>dv</math> integration over all space | ||
Revision as of 03:32, 22 November 2007
Fermi's Golden rule is used to calculate the probability (per unit time) of a quantum mechanical transition between two quantum states. Although Fermi first coined the term "Golden Rule", Dirac developed most of the machinery.
The first part of the Golden rule is the transition matrix element
where
- = initial quantum state of the system
- = final quantum state of system after a transition
- = the part of the total Hamiltonian () which describes the interaction responsible for the transition.
- = Unperturbed ("steady state") Hamiltonian
- = total Hamiltonian describing the quantum mechanical system
- integration over all space