Modern Physics

# Schrodinger time independent wave equation derivation

Schrodinger time dependent wave equation

## What is schrodinger wave equation?

In classical mechanics the motion of a body is given by Newton’s second law of motion.But elementary particles like electron,protons and photons possess wave properties as well,therefore another equation instead of Newton’s second law equation ( F=ma) is required for describing their motion.The new equation must take into account wave properties of particles and it should therefore be similar to equation describing wave on strings acoustic waves or electromagnetic waves.This equation was found in 1926 by the Austrian physicist schrodinger and is known after his name as schrodinger equation.

## Schrodinger wave equation derivation

Consider a particle of mass “m” moving with velocity “v” in space.Suppose a system of  stationary waves is associated with the particles at any point in space in the neighborhood of particle.

We know that:   This is the schrodinger time independent wave equation.