No abstract

No abstract

No abstract

No abstract

No abstract

An exactly solvable problem for the finite-difference Schrödinger equation in the relativistic configurational space is considered. The appropriate finite-difference generalization of the factorization method is developed. The theory of new special functions ‘‘the relativistic Hermite polynomials,’’ in which the solutions are expressed, is constructed.

Abstrac t. For a three-dimensional model of the harmonic oscillator in the relativistic configurational r-representation wave functions in the spherical coordinates r = (r, 0, q~) are found. The generating function, orthogonality and various recurrence relations for the radial part of the wave function are obtained. The radial and orbital quantum numbers raising and lowering operators are defined and the dynamical symmetry group is constructed by means of the Infeld-Hull factorization method.Ein relativistisches Modell des isotropen Oszillators I n h a l t s u b e r s i c h t . Fur ein dreidimensionales Modell des harmonischen Oszillators werden in der rclntivistischen r-Darstellung Wellenfunktionen in spharischen Koordinaten r = (r, 0 ,~) gefunden. Es wcrden die erzeugende Funktion, Orhogonalitats-und verschiedene Rekursionsrelationen fur den radialen Teil der Wellenfunktion erhalten. Die Operatoren, die die radialen und orbitalen Quontenzahlen erhohen oder erniedrigen, werden definiert und die dynamische Symmetriegruppe wird mittels der Infeld-Hull-Faktorisierungsmethode konRtruiert .

No abstract