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Explain briefly the time independent Schrodinger wave equation. S |
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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 dependingon the field of force in which the electron moves. The time independent Schrodinger equation can be expressedas , `hat(H) Psi=E Psi` Where `hat(H)`is called Hamiltonian operator, `Psi ` is the wave funcation and is a function of position co-ordinates ofthe particle and is denoted as `Psi`(X, Y, Z)E is the energy of the system `hat(H) = [(-h^(2))/(8pi^(2) m)((del^(2))/(delx^(2))+(del^(2))/(dely^(2))+(del^(2))/(delz^(2)))+ V ]` can be written as, `[(-h^(2))/(8pi^(2)m)((del^(2)Psi)/(delx^(2)) +(del^(2)Psi)/(delx^(2)) +(del^(2)Psi)/(delz^(2)))+V Psi ] = E Psi` Multiply by ` - (8 pi^(2) m)/(h^(2)) `and rearranging `(del^(2)Psi)/(delx^(2)) + (del^(2)Psi)/(dely^(2))+(del^(2)Psi)/(delz^(2))+(8 pi ^(2) m)/(h^(2)) (E - V) Psi = 0 ` The above schrodingerwave equation does not containtime as a variable and is referred to as time independent Schrodinger wave equation . |
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