Schrodinger Wave Equation
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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 relationship

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


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,


Where


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


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

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

Substituting the values of


Or


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