# Spherical symmetry

1. Sep 19, 2012

### rubertoda

I have a problem; I am trying to show the spherical symmetry in a hydrogen atom, for a sum over the l=1 shell i.e the sum over the quadratics over three angular wave equations in l=1,

|Y10|^2 + |Y11|^2 + |Y1-1.|^2 .

This should equal up to a constant or a zero to yield no angular dependence. m goes from -l to l.

The problem is that when trying to do this, i get all kinds o different sin, cos formulas, which i cannot reduce to zero or a constant to make the total equation only radial dependent - or am i doing this the wrong way?

Anyone who did this problem?

Last edited: Sep 19, 2012
2. Sep 19, 2012

### gabbagabbahey

It sounds like you have the correct approach. Why don't you show us your calculation so we can tell you where you are going wrong.

3. Sep 19, 2012

### rubertoda

I have: $$|\frac{1}{2}\sqrt{3/2\pi}\sin\theta e^{-i\delta}|^2+|\frac{1}{2}\sqrt{3/2\pi}\sin\theta e^{i\delta}|^2 + |\frac{1}{2}\sqrt{3/\pi}\cos\theta|^2$$

which i finally got to: $$\frac{3}{4\pi}((\cos\theta)^2 + (\sin\theta)^2((\cos\delta)^2 - (\sin\delta)^2)$$

which i obviously cannot get to a constant or zero.

4. Sep 19, 2012

### gabbagabbahey

The deltas should disappear when you take the modulus of each term. For a complex number, the modulus is defined as $|z|=\sqrt{zz^*}$, you don't just square the number, you multiply by its complex-conjugate.