Hydrogen atom in a magnetic field as an exactly solvable system without dynamical symmetries?

• According to the generally accepted classification, there are supersymmetric superintegrable systems for which the Schrödinger equation is separable in more than one coordinate system and which admit an exact solution. A classic example of a superintegrable system is a hydrogen atom. It is believed that the converse is also true: an exactly solvable system has many integrals of motion corresponding to the separation constants of the Schrödinger equation in more than one coordinate system, which also means a high symmetry group of the system. It is shown that the existence of an exact solution for a hydrogen atom in an arbitrary strong uniform magnetic field apparently contradicts this classification.

Ämnesord

NATURVETENSKAP  -- Fysik -- Annan fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Other Physics Topics (hsv//eng)

NATURVETENSKAP  -- Fysik -- Astronomi, astrofysik och kosmologi (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Astronomy, Astrophysics and Cosmology (hsv//eng)

Nyckelord

Exact solution

Hydrogen atom

Integrability

Magnetic field

Superintegrability

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