# Finding Quantum numbers from wavefunction

1. Nov 25, 2013

### andre220

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

Consider a spinless particle in a central field in a state described by:
$$\psi_a(r) = (x^2 - y^2) e^{-\alpha r^2}$$
$$\psi_b(r) = xyz e^{-\alpha r^2}$$

Find quantum numbers $$l$$ and $$l_z$$ (or their appropriate superposition) for these two cases.

2. Relevant equations

$$\psi(r) = \psi(r, \theta, \phi) = R(r)Y(\theta, \phi)$$

3. The attempt at a solution

Okay so I am not sure where to start with this problem, I could construct the Schrodinger equation in terms of the radial and spherical harmonics and then we know that $$l$$ can be determined from this equation, yet I do not know what the potential for such equation should be.

2. Nov 25, 2013

### vela

Staff Emeritus
You don't need to use the Schrodinger equation. Express the wave functions in spherical coordinates and separate it into an angular part and a radial part. You want to express the angular part as a linear combination of the spherical harmonics.