What is the Free particle Wave equation?
Derive Energy and momentum operator with the help of Free particle Wave equation
Free particle Wave equation:
If we assume that matter waves are produced due to variation in the wave function similarly as sound waves are produced due to variation in pressure and electromagnetic waves are produced due to variation in electric and magnetic fields. The wave function is a function of both the position and time. Now, let us assume that wave function for the wave moving along positive x-direction can be represented as
This is the free particle wave equation.
Energy and momentum operator:
On partially differentiating with respect to t to equation (3), we get