Question

prove the schrodinger wave equation​

Answer 1

Explanation:

Describing the wave motion of a particle along x axis is given by

psi=Asin2π x/lambda

Differentiating psi w.r.t.x ,we get

dpsi/dx=Acos2 I x/lambda(2π/lambda)

=2πA/lambda.cos2π x/lambda

Again differentiating

d^2psi/dx^2=2πA/lambda(-sin2π x/lambda)2π/lambda

=-4π^2/(lambda)^2(Asin2π x/lambda)

=d^2psi/dx^2+4π^2/lambda^2psi=0

if the electron move along x,y,z axis then

d^2psi/dx^2+d^2psi/dy^2+d^2psi/dz^2+4π^2psi/lambda^2=0

=del^2psi+4π2psi/lambda^2=0

acc debroglie ,lambda =h/mv

1/lambda^2=m^2v^2/h^2

m^2v^2/h^2=-del^2.1/4π^2psi

k.E=-del^2psi h^2/8π^2psi m

so the Schrodinger wave equation is

del^2psi+8π^2m/h^2(E-P.E)psi=0