# Hydrogen atom. Simple question I think.

1. May 8, 2013

### LagrangeEuler

When you solving Sroedinger eq for hydrogen atom you get energy values $E_n\approx \frac{1}{n^2}$. Why for some value of this energy electron don't leave atom?

2. May 8, 2013

### Staff: Mentor

Because the minimum energy needed to remove the electron, the ionization energy, is obtained from
$$IE = \lim_{n \rightarrow \infty} E_n$$

Another way to put it is that you have an infinite number of bound states, where the total energy (kinetic + potential) is lower than the energy necessary to remove the electron.

3. May 8, 2013

### bahamagreen

Maybe because a square wave is not a solution to the equation.

4. May 9, 2013

### tom.stoer

The bound states have negative (!) energies $E_n\approx -\frac{1}{n^2}$

The (continuum) scattering states have positive energies; they correspond to umbound electrons.