A singular Lambert-W Schrödinger potential exactly solvable in terms of the confluent hypergeometric functions / A. Ishkhanyan
Уровень набора: Modern Physics Letters A, Scientific Journal = 1986-Язык: английский.Страна: .Резюме или реферат: We introduce two potentials explicitly given by the Lambert-W function for which the exact solution of the one-dimensional stationary Schrödinger equation is written through the first derivative of a double-confluent Heun function. One of these potentials is a singular potential that behaves as the inverse square root in the vicinity of the origin and vanishes exponentially at the infinity. The exact solution of the Schrödinger equation for this potential is given through fundamental solutions each of which presents an irreducible linear combination of two confluent hypergeometric functions. Since the potential is effectively a short-range one it supports only a finite number of bound states..Примечания о наличии в документе библиографии/указателя: [References: 47 tit.].Тематика: электронный ресурс | труды учёных ТПУ | уравнение Шредингера | гипергеометрические функции | квадратные корни | бесконечность Ресурсы он-лайн:Щелкните здесь для доступа в онлайнTitle screen
[References: 47 tit.]
We introduce two potentials explicitly given by the Lambert-W function for which the exact solution of the one-dimensional stationary Schrödinger equation is written through the first derivative of a double-confluent Heun function. One of these potentials is a singular potential that behaves as the inverse square root in the vicinity of the origin and vanishes exponentially at the infinity. The exact solution of the Schrödinger equation for this potential is given through fundamental solutions each of which presents an irreducible linear combination of two confluent hypergeometric functions. Since the potential is effectively a short-range one it supports only a finite number of bound states.
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