Question

Derive the schrodinger wave equation for hydrogen atom?

Answer 1

Schrodinger equation can be solved completely for hydrogen atoms as well as hydrogen type atoms, like atoms (ions)

It is solved by accounting cartesian coordinates x, y and z that are converted to polar coordinates r, θ and ɸ.

The Schrodinger equation is given by,

$\bigtriangledown^2$ψ+$\frac{8\pi^2m}{h^2}$(E-V)ψ=0

Cartesian coordinates are given by,

z = r cos θ

y = r sin θ sin Φ

x = r sin θ cos Φ

$\bigtriangledown^2\psi =\frac{\partial^2 \psi}{\partial x^2}+\frac{\partial^2 \psi}{\partial y^2}+\frac{\partial^2 \psi}{\partial z^2}$

Then,