Quantization and the hydrogen atom

J. Elhadad

M. Sağlam, Ziya Saglam, Boyacioglu B. .

J.P. MATHIEU

Sangwha Yi

The article treats that the quantization in the Bohr’s theory about the hydrogen atom. If calculates the electron motion in the hydrogen atom by the classical mechanic, can do the quantization in the Bohr’s theory about the hydrogen atom. In this time, the electron’s orbit velocity is non-relativity velocity.

Eduardo V. Flores

Toshihiro Iwai

Quantization of the conformal Kepler problem is defined and studied in order that the quantized system, which will be referred to as a conformal hydrogen atom, may associate the harmonic oscillator with the hydrogen atom. The conformal hydrogen atom shares with the harmonic oscillator the eigenspaces of negative energies. The four-dimensional conformal hydrogen atom reduces to the three-dimensional ordinary hydrogen atom. The symmetry group SO(4) of the hydrogen atom is brought out from the symmetry subgroup of the harmonic oscillator. The conformal hydrogen atom gives an example of those quantum systems of which the configuration spaces are curved Riemannian spaces with nonconstant scalar curvatures and of which the Hamiltonian operators depend on the scalar curvatures.