A conditionally exactly solvable generalization of the inverse square root potential

A. M. Ishkhanyan

Результат исследований: Материалы для журналаСтатьярецензирование

14 Цитирования (Scopus)


We present a conditionally exactly solvable singular potential for the one-dimensional Schrödinger equation which involves the exactly solvable inverse square root potential. Each of the two fundamental solutions that compose the general solution of the problem is given by a linear combination with non-constant coefficients of two confluent hypergeometric functions. Discussing the bound-state wave functions vanishing both at infinity and in the origin, we derive the exact equation for the energy spectrum which is written using two Hermite functions of non-integer order. In specific auxiliary variables this equation becomes a mathematical equation that does not refer to a specific physical context discussed. In the two-dimensional space of these auxiliary variables the roots of this equation draw a countable infinite set of open curves with hyperbolic asymptotes. We present an analytic description of these curves by a transcendental algebraic equation for the involved variables. The intersections of the curves thus constructed with a certain cubic curve provide a highly accurate description of the energy spectrum.

Язык оригиналаАнглийский
Страницы (с-по)3786-3790
Число страниц5
ЖурналPhysics Letters, Section A: General, Atomic and Solid State Physics
Номер выпуска45
СостояниеОпубликовано - 25 ноя 2016

ASJC Scopus subject areas

  • Physics and Astronomy(all)

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