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Hydrogen Solution Calculator

Shodor > CSERD > Resources > Models > Hydrogen Solution Calculator

  Software  •  Instructions  •  Theory

Instructions - Hydrogen Solutions Calculator


This applet creates an equation which is the solution to Schrodinger's equation for Hydrogen with a single electron.

What is returned to the user is

\Psi(l\vert m=0\vert n, \vec{r})^*\Psi(l\vert m=0\vert n, \vec{r})

where $\Psi$ solves the equation

\mathbf{H} \Psi(\vec{r}) \equiv
=E \Psi(\vec{r})

for a potential of $V(r)=e^2/r$.

The magnitude of the wave is not normalized, and the radial variable is normalized such that r in this problem has been multiplied by $2 \sqrt{E}$. The energy level is related to the actual energy of the electron by

\nu = - \frac{m e^2}{\sqrt{e} \hbar^2}


\nu = l + 1 + n

and the scaled radial variable $x = 2 \sqrt{E}$ solves the equation


In addition, the user can select to see the real or imaginary portions of the solution, as well as the Associated Legendre function or the radial solution for the given energy levels.


Select the desired solution from the wavefunction, the Legendre functions, or the radial solution.

Select the value of l, m, and n for which you would like to see a solution.

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