Hydrogen atom. Simple question I think.

[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?

 

[DrClaude]

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.

 

[bahamagreen]

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

 

[tom.stoer]

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?

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.