# Wavefunction and shroedinger equation

1. Sep 27, 2014

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

2. Relevant equations

3. The attempt at a solution

First, I got the wavefunction to look like the one in the question. I think the wavefunction should be n=1 not n=0. So Y(theta,psi) = A constant, that is where the C comes from. But how can I plug this into the shrodinger equation? How can I answer this question?

2. Sep 27, 2014

### ShayanJ

In the Schrodinger equation, there is a differentiation operator ($-\frac{\hbar^2}{2m} \nabla^2$ )and a multiplication-by-a-function($-\frac{kZe^2}{r}$) operator. You just should apply those operators to $\phi_{0,0,0}(\vec r)$ and add the results and check whether you get a constant times $\phi_{0,0,0}(\vec r)$.
For $-\frac{\hbar^2}{2m} \nabla^2$, you should first take the gradient of $\phi_{0,0,0}(\vec r)$ which gives you a vector field which you should get the divergence of. Then multiply by $-\frac{\hbar^2}{2m}$.

3. Sep 28, 2014

### Orodruin

Staff Emeritus
Alternatively to the two step approach in first taking the gradient and then the divergence of the gradient, you could apply the Laplace operator in spherical coordinates directly:
$$\nabla^2 = \frac{1}{r^2}\frac{\partial}{\partial r} r^2 \frac{\partial}{\partial r} = \frac{\partial^2}{\partial r^2} + \frac{2}{r} \frac{\partial}{\partial r} ,$$
where I have removed the angular part since your wave function does not depend on the angles.