Modern Physics

Schrodinger time dependent wave equation

Schrodinger time-dependent wave equation is a partial linear differential equation that describes the state function or wave function of a quantum mechanics system. It is a very important result in quantum mechanics or modern physics. This equation presented by Ervin Schrodinger in 1925 and published in 1926.

Schrodinger time-dependent wave equation derivation

Consider a particle of mass “m” with velocity “v” and under the influence of potential energy (P.E) which is represented by V(r) . The total energy of the particle is the sum of potential energy (P.E) and kinetic energy (K.E) which is given by:
schrodinger wave equation derivation
schrodinger wave equation
schrodinger wave equation
 
schrodinger wave equation
time dependent schrodinger wave equation
 
 
schrodinger time dependent wave equation formula
This is the Schrodinger time-dependent wave equation formula.
The factor hamiltonian operator formula=H is known as a Hamiltonian operator which gives the energy of the particle. Now equation (7) can be written as:

time dependent schrodinger wave equation in general form
See also : Schrodinger time-independent wave equation
 

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