# Wavefunctions of hydrogen

1. May 2, 2014

### unscientific

1. The problem statement, all variables and given/known data

What quantum numbers are used to define state of hydrogen? The wavefunction has no angular dependence. Find the values of all the angular momentum quantum numbers for the electron.

2. Relevant equations

3. The attempt at a solution

The numbers are n, l and m.

n: Energy level
l(l+1): Eigenvalues of total orbital angular momentum
m: z component of orbital angular momentum

The complete wavefunction is given by: $\psi = u_n^l Y_l^m$.

Thus the only spherical harmonic that doesn't have angular dependence is $Y_0^0 = \sqrt{\frac{1}{4\pi}}$.

Thus the wavefunctions are $\sqrt{\frac{1}{4\pi}}u_n^0$.

Thus n = any integer, l = 0, m = 0.

I'm slightly bothered by the term 'spatial part' of the wavefunction.

2. May 3, 2014

### BvU

"Spatial part" as opposed to "spin part". The exercise probably doesn't want you to worry about spin (my guess -- change that if you just finished a chapter on spin...)

3. May 3, 2014

### unscientific

We learn about the gross structure of Hydrogen, which ignores spin as the Hamiltonian is the KE of the nucleus and electron, and the potential energy.