THE HYDROGEN ATOM

Application of the Schrodinger equation to the hydrogen atom

1

Solution may be a product of three functions

2

Equation is separable

Solution of the Schrodinger Equation of Hydrogen atom

Azimuthal equation 3

Radial Equation r

Angular equation a

Predicted energy level predi

Hydrogen atom radial wave functions box

Solution of the Angular and Azimuthal
Equations sol

Spherical harmonics spheri

Quantum numbers

ml(Magnetic quantum number) mag

Quantized energy qe

Orbital angular momentum quantum number (l)

Principal Quantum number( n)

n= 1,2,3,4...

n>0

l= 0,1,2,3,....(n-1)

l<n

ml=-l,-l+1,....0,1,...,l-1,l

|ml| less-than or equal to l

Magnetic Effects on Atomic Spectra—The
Normal Zeeman Effect fz vb z2 z1 z3

Intrinsic Spin s ss

The gyro-magnetic ratio gro

Energy Levels and Electron Probabilities

Probability Distribution Functions immm 111 222

The probability density for the hydrogen atom for three different electron states hydro

Selection rule selru