Time-Dependent 4D Quantum Harmonic Oscillator and Reacting Hydrogen Atom

With the help of low-dimensional reference equations (ordinary differential equations) and corresponding coordinate transformations, non-stationary 4D quantum oscillator in an external field is reduced to autonomous form. The latter, particular, reflects existence a new type dynamical symmetry that reduces equation motion form does not change with time. By imposing additional constraint on wave function isotropic oscillator, we have obtained total functions reacting hydrogen atom two different cases: (a) when frequency has asymptotic values there no field; (b) when, addition frequency, force acts atom. transition S-matrix elements various elementary atomic–molecular processes are constructed. probabilities transitions others, including bound states, studied detail, taking into account influence forces.