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Explain briefly the time independent schrodinger wave equation? |
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Answer» Solution :Erwin Schrodinger expressed the wave nature of electron in terms of a differential EQUATION. This equation determines the change of wave FUNCTION in space depending on the field of FORCE in which the electron moves. The time independent Schrodinger equation can be expressed as, `hatH PSI = EPsi` Where `hatH` is called Hamiltonian operator, `Psi` is the wave function and is a function of position co-ordinates of the particle and is denoted as `Psi(x, y,z) E` is the energy of the system `hatH = [(-h^2)/(8pi^2m)((del^2)/(del x^2) + (del^2)/(del y^2) + (del^2)/(del z^2)) + V ]` Can be written as, `[(-h^2)/(8pi^2m)((del^2Psi)/(del x^2) + (del^2Psi)/(del y^2) + (del^2Psi)/(del z^2)) + VPsi ] = EPsi` Multiply by `-(8 pi^2.m)/(h^2)` and rearranging `(del^2 Psi)/(del x^2) + (del^2Psi)/(dely^2) + (del^2Psi)/(delz^2) + (8pi^2m)/(h^2) (E - V) Psi = 0` The above schrodinger wave equation does not contain time as a variable and is refferred to as time independent Schrodinger wave equation. |
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