Question

Quantum Mechanics :

(Selection rule) Discuss the physical basis for the selection rule that a transition from one state of angular momentum zero to another state of angular momentum zero by emitting a photon, is forbidden.

Answer 1

In quantum mechanics the basis for selection rule is determined by ffinding the value of the transition moment integral

$\int {\psi}_1^*\mu\psi_2d\tau$

Now $$ {\psi}_1 $ and \psi_2$ ​​​​​ are the wave function of the two states involved in the transition and $\mu$ is the transition moment operator. This integral represent the propagator of the transition between states. Therefore if the value of this integral is zero then the transition is forbidden. Now for j=0 to j=0 states the value of this integral is calculated to be zero. So this transition is forbidden in the selection rule.