## Schrodinger Wave Equation

**Schrodinger Wave Equation** Assignment Help | **Schrodinger Wave Equation** Homework Help

# Schrodinger Wave Equation

In the light of de Broglie concept of dual character of dual character of matter and the Heisenberg’s uncertainty principle, Bohr’s concept of definite trajectories (orbits) failed. Thus like any other wave, it would be possible to express the motion of the electron in terms of an equation, called the wave equation. The derivation of this equation was carried out by Schrodinger in 1926, making use of thede Broglie relationshipwhich, therefore, may be called the essential postulate of Schrodinger wave equation. The derivation may be carried out as follows:

Consider the simplest type of wave motion like that of the vibration of a stretched string traveling along the x-axis with a velocity u

Vibration of a Stretched string

If is the amplitude of the wave at any point whose co-ordinate is x, at any time t, then the equation of such a wave motion is

This differential equation indicates that the amplitude of the wave at any time traveling with a particular velocity depends upon the displacement x and the time t. In other words, is function of x and t. Hence we may write

Where is a function of the co-ordinate x only and is a function of the time t only.

But for the stationary waves.*as occur in the stretched string, we know that

Where v is the frequency of vibration and A is a constant, equal to the maximum amplitude of the wave.

Subsisting the value of (from eqn. in eqn. we get

Differentiating this equation twice w.r.t, we get

Differentiating eqn. twice w.r.t. x, we get

Substituting the values of and form equations and into the equation we get

Or

For more help in

**Schrodinger Wave Equation**click the button below to submit your homework assignment