Question

What is the probability function for the Hydrogen atom?

Answer 1

The wave function of an electron gives the information about the electron in an atom. The wave function `psi` is specified by a set of 3 quantum numbers which arise as a natural consequence of solving the Schrödinger wave equation. Together, with the spin quantum number, it defines the quantum state of an electron in an atom.

The wave function `psi` is physically insignificant. The square of the wave function `psi^2` is equal to the probability density (probability per unit volume) of finding an electron in a point.

Thus, the probability of finding an electron at a given point is, `delV*psi^2`.

This is not only true for a hydrogen atom but, for any atom or any quantum mechanical system.

In case of hydrogen atom, however, the energy of the electron depends only on the value of the principle quantum number `n`.