X-Nico

Hydrogen atom

The solution of the Schrödinger equation (wave equations) for the hydrogen atom uses the fact that the Coulomb potential produced by the nucleus is isotropic (it is radially symmetric in space and only depends on the distance to the nucleus).

First quantization

For example, the three quantum numbers $n,l,m$ associated to an electron in a coulomb potential, like the hydrogen atom, form a complete set (ignoring spin).

Good quantum number

In the case of the hydrogen atom (with the assumption that there is no spin-orbit coupling), the observables that commute with Hamiltonian are the orbital angular momentum, spin angular momentum, the sum of the spin angular momentum and orbital angular momentum, and the $z$ components of the above angular momenta.

Laplace–Runge–Lenz vector

The hydrogen atom is a Kepler problem, since it comprises two charged particles interacting by Coulomb's law of electrostatics, another inverse square central force.

Protonium

Unlike the hydrogen atom in which the dominant interactions are due to the Coulomb attraction of the electron and the proton, the constituents of protonium interact predominantly through the strong interaction.

Unit fraction

An explanation for this phenomenon is provided by the Bohr model, according to which the energy levels of electron orbitals in a hydrogen atom are inversely proportional to square unit fractions, and the energy of a photon is quantized to the difference between two levels.

see also

Ramachandran plot

Glycine has only a hydrogen atom for its side chain, with a much smaller van der Waals radius than the CH₃, CH₂, or CH group that starts all other amino acids.

Unit fraction

The energy levels of photons that can be absorbed or emitted by a hydrogen atom are, according to the Rydberg formula, proportional to the differences of two unit fractions.