# Physics Group - II (3110018)

BE | Semester-1   Winter-2019 | 02-01-2020

## Q4) (a)

#### Discuss Fermi golden rule.

• In quantum physics, Fermi’s golden rule is used to calculate transition rates. The transition rate depends upon the strength of coupling between the initial and final state of a system and upon the number of ways the transition can happen (joint density of states).
• The transition probability is given by:

Where, ${\mathrm{\lambda }}_{\mathrm{if}}$ is transition probability,  is matrix element for interaction and ${\mathrm{Z}}_{\mathrm{f}}$ is joint density of final state.

• The above equation is known as fermi’s golden rule.
• The transition probability $\mathrm{\lambda }$ is called the decay probability and is related to mean lifetime $\tau$ of the state.

• The general form of fermi’s golden rule can be applied to atomic transitions. Nuclear decay and scattering.
• This coupling term is traditionally called the matrix element for the transition.
• This matrix element can be placed in the form of an integral, where the interaction (that causes transition) is expressed as a potential v that operates on initial state wave function.
• The transition probability is proportional to the square of integral of interaction over all of the space appropriate to the problem.

Where, V is operator for physical interaction that couples initial and final states, ${{\mathrm{\psi }}^{*}}_{\mathrm{f}}$ is wave function for final state and is wave function for initial state.