Schrodinger Wave Equation

SCHRODINGER WAVE EQUATION

Schrodinger wave equation describes the wave nature of a particle in mathematical form. It is the basic equation of motion for matter waves.

If the particle has wave properties, then there should be some sort of wave equation to describe the behaviour of that particle.

Schrodinger connected the expression of de-Broglie's wavelength with the classical wave equation for a moving particle. He obtained a new wave equation. This wave equation is known as Schrodinger wave equation.

Forms of Schrodinger wave equations

There are two forms of Schrodinger wave équations.

They are:

(a) Time independent wave equation 

(b) Time dependent wave equation

One, which is general and takes care of both the position and the time variations of the wave function, is called time-dependent Schrodinger equation.

It involves the imaginary quantity ‘i’.

The other one is applicable only to steady state conditions in which case, the wave function can have variation only with position but not with time. It is called time-independent Schrodinger's equation and is simpler than the other one. It doesn't involve ‘i’.

Accordingly we get the corresponding wave functions by solving the respective types of schrodinger equation. The wave functions obtained as solutions of time-dependent schrodinger equation will always be complex.

But the wave functions obtained as solutions of timeindependent schrodinger equation are not necessarily complex functions, though they could be complex under certain conditions.