Modern Physics

Schrodinger time dependent wave equation

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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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