Engineering Physics: Unit IV: Basic Quantum Mechanics

Schrodinger Time Dependent Wave Equation

Schrodinger time dependent wave equation is derived from Schrodinger time independent wave equation.

SCHRODINGER TIME DEPENDENT WAVE EQUATION

Schrodinger time dependent wave equation is derived from Schrodinger time independent wave equation.

The solution of classical differential equation of wave motion is given by


Differentiating eqn (1) with respect to time t, we get out 


Multiplying i on both sides in eqn (4), we have


Schroedinger time independent wave equation is


Substituting for EΨ from eqn (5)

The eqn (7) is known as Schrodinger time dependent wave equation.

Note: In eqn (7), there is term representing time. That is why it is called time dependent wave equation.


Engineering Physics: Unit IV: Basic Quantum Mechanics : Tag: : - Schrodinger Time Dependent Wave Equation