Discretization of Natanzon potentials

Discretization of Natanzon potentials

Бібліографічні деталі
Parent link:The European Physical Journal Plus
Vol. 131.— 2016.— [342, 11 p.]
Автор: Ishkhanyan A. Artur
Співавтор: Национальный исследовательский Томский политехнический университет Физико-технический институт Кафедра общей физики
Інші автори: Kraynov V. Vladimir
Резюме:Title screen
We show that the Natanzon family of potentials is necessarily dropped into a restricted set of distinct potentials involving a fewer number of independent parameters if the potential term in the Schrцdinger equation is proportional to an energy-independent parameter and if the potential shape is independent of both energy and that parameter. In the hypergeometric case only six such potentials exist, all five-parametric. Among these, only two (Eckart, Pцschl-Teller) are independent in the sense that each cannot be derived from the other by specifications of the involved parameters. Discussing the solvability of the Schrцdinger equation in terms of the single-confluent Heun functions, we show that in this case there exist in total fifteen seven-parametric potentials, of which independent are nine. Six of the independent potentials present different generalizations of the hypergeometric or confluent hypergeometric ones, while three others do not possess hypergeometric sub-potentials. The result for the double- and bi-confluent Heun equations produces the three independent double- and five independent bi-confluent six-parametric Lamieux-Bose potentials, and the general five-parametric quartic oscillator potential for the tri-confluent Heun equation.
Режим доступа: по договору с организацией-держателем ресурса
Мова:Англійська
Опубліковано: 2016
Предмети:
электронный ресурс
труды учёных ТПУ
дискретизация
потенциалы
Онлайн доступ:http://dx.doi.org/10.1140/epjp/i2016-16342-9
Формат: Електронний ресурс Частина з книги
KOHA link:https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=651784

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