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:

                         λif = 2π  Mif 2 Zf 

    Where, λif is transition probability,  Mif 2 is matrix element for interaction and Zf is joint density of final state.

  • The above equation is known as fermi’s golden rule.
  • The transition probability λ is called the decay probability and is related to mean lifetime τ of the state.

                         λ = 1τ 

  • 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.

                         Mif = ψ*f · V · ψ i ·dv 

    Where, V is operator for physical interaction that couples initial and final states, ψ*f is wave function for final state and ψ i is wave function for initial state.