# Normalizaed wave function of the hydrogen atom

1. Dec 5, 2005

### asdf1

how do you find the normalized wave functions of the hydrogen atom for n=1, l=0 and ml=0?
in my textbook, it's a table, but i have no idea where the figures come from...

2. Dec 5, 2005

### Staff: Mentor

You do it by finding the solution for the Schrödinger equation for the hydrogen atom. This means finding the solutions of the individual differential equations for the functions $R(r)$, $\Theta(\theta)$ and $\Phi(\phi)$.

Many introductory textbooks work through the solution for $\Phi(\phi)$ because its equation is rather easy. But I didn't see the complete solution for $\Theta(\theta)$ and $\Phi(\phi)$ until my graduate school QM courses. They're that messy! :yuck:

Oh wait, I was thinking of the general solution for any n, l, m. You want specifically n=1, l=0, m=0. That case might not be too bad, after you substiute those values of n, l, m into the individual differential equations for the three variables. $\Theta(\theta)$ and $\Phi(\phi)$ both turn out to be constant in this case, so their differential equations must be very simple!

Last edited: Dec 5, 2005
3. Dec 5, 2005

### asdf1

$\Theta(\theta)$
but the original function isn't known, right? so how do you solve it?

4. Dec 5, 2005

### Staff: Mentor

That's what the Schrödinger equation is for, or rather the individual ordinary differential equations that you get after you separate the S.E.

Solving an algebraic equation like $x^2 - 5x + 6 = 0$ gives you a number for $x$, or a set of numbers. Solving a differential equation like $d^2 \Phi(\phi) / d \phi^2 = -m_l^2 \Phi(\phi)$ gives you a function for $\Phi(\phi)$, or a set of functions.

5. Dec 6, 2005

### asdf1

thank you very much!!! :)