Comments on the one-dimensional hydrogen atom [Am. J. Phys. 2 7, 649 (1959); Am. J. Phys. 3 7, 1145 (1969); Am. J. Phys. 4 4, 1064 (1976)

Abstract

Extraneous solutions to the Schroedinger equation are discussed. (AIP)

Strong-field phenomena caused by ultrashort laser pulses: Effective one- and two-dimensional quantum-mechanical descriptions

“…As early as 1959, in Ref. [54], as well as in later works [55,56], wave functions of the stationary states in the solid-core potential were studied. Later, the solidcore potential was used to describe the Coulomb interaction between charge carriers encapsulated in quasi-1D nanostructures, which are quantum dots and quantum wires (see Refs.…”

Regularization of Quantum Tunneling of Singular Potential Barrier

“…The same result was obtained by the method of limiting smoothing of the potential barrier and led to the conclusion that under a physically acceptable interpretation of the singularity, the one-dimensional Coulomb potential is impenetrable. The conclusion was then supported by C. Hammer and T. Weber during the presentation of a short letter [4]. Further, M. Moshinsky, considering unbounded states of an antisymmetric one-dimensional Coulomb potential [5], considers it preferable not to discard an irregular solution, but to transform it by a certain procedure into a regular one.…”

Relativistic one-dimensional hydrogen atom in momentum representation

“…impurities and excitons in semiconductors, quantum well structures and hydrogen atoms in strong magnetic fields. Nevertheless this problem, that could be thought of as easy, has become polemic due to the possible existence of degenerate levels and of a ground state with an infinite binding energy (Moss 1987, Hammer andWeber 1988).…”