## Schrodinger time independent equation:

Let us consider an electron of mass 'm' moving with velocity 'V'. As the electron is spreading like a wave, its wave length is given by

Let the differential equation for probability of electron is given by

Solution for the above differential equation is

by partially differentiating with respect to time on both the sides, we get

by re-differentiating, we get

by substituting Eq - (2) we get,

by substituting the above equation in Eq - (1) we get,

Now let us consider

Now substituting the above value in equation 3 we get,

We know that the total energy is the sum of kinetic energy and potential energy

Substituting this equation in equation - (4)

As time is not involved in this equation, it is known as Schrodinger time independent equation.

## Schrodinger time dependent equation

By eliminating the energy term E from this we get Schrodinger time dependent equation. We know that the solution for the differential equation is

Partially differentiating with respect to time 't' on both the sides we get,

Schrodinger time independent equation is,

This equation can be written as,