# Radial part of wave function in respect to spherical harmonic

#### Zaknife

1. Homework Statement
Consider a Wavefunction:
$$\psi(x,y,z)=K(x+y+x^2-y^2)e^{-r/a}$$
Find expectation value of $$L^{2} , L_{z}^{2}, L_{x}^{2}$$.

2. Homework Equations

3. The Attempt at a Solution
The first step would be a rewriting a wavefunction in terms of spherical coordinates:
$$\psi=Kr(\cos\phi \sin \theta + 2 \sin \phi \cos \theta +r(\cos^{2} \phi \sin^{2} \theta - \sin^{2} \phi \sin^{2} \theta ))$$

My Question is : is it fair to skip the radial part and just forget about it. Normalize the Wavefunction for just the angular part , and then consider a mean values of Angular Momentum Operators ? Or should i normalize the wavefunction including r ? It bothers me because of the r squared in the equation.

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#### vela

Staff Emeritus
Homework Helper
You can't neglect the radial functions.

#### Zaknife

Just to make it clear - i need to do all next steps with the radial part ?

Staff Emeritus