 Mauro Murzi's pages on Philosophy of Science - Quantum mechanics
Bohr energy levels

# [3. Schrödinger equations.]

## Bohr energy levels.

In Bohr theory of the hydrogen atom, the angular momentum of the electron in its orbit is a multiple of the quantity h/2π, so the energy of the electron is quantized. The values En of the energy of the electron, called the energy levels, are given by the formula .

This formula is derivable from the first Schrödinger equation. Consider an application of the equation (3.7) to the hydrogen atom: The expression for the potential U is U = - e²/r where e is the electron charge and r is the distance from the electron. In polar coordinates the equation (3.7) became where Ω(r) is a function of the distance r. The eigenvalues of the equation (3.9) are the values of E given by equation (3.8). Thus the first Schrödinger equation gives a correct deduction of the energy levels of Bohr theory. Values of E different from series (3.8) generate solutions Ω(r) not acceptable. The figure shows the diagram of four solutions, two acceptable and two not acceptable.