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 in a similar manner 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