Exact solutions of a nonpolynomial oscillator related to isotonic oscillator

  • Qian Dong
  • Guo-Hua Sun
  • N. Saad
  • Shi-Hai DongEmail author
Regular Article


We find that the analytical solutions to a quantum system with a nonpolynomial oscillator potential related to isotonic oscillator are given by the confluent Heun functions \( H_{c}(\alpha, \beta, \gamma, \delta, \eta; z)\). The properties of the wave functions, which are strongly relevant for the potential parameters a and g, are illustrated. It is shown that the wave functions are shrunk to the origin for a given a when the potential parameter g increases, while the wave peak of wave functions is concaved to the origin when the negative potential parameter \( \vert g\vert\) increases. Moreover, the wave peaks of the even wave functions become sharper when the potential parameter \( a < 1\) decreases, but they become flat when the potential parameter \( a > 1\) increases. When the minimum value \( V_{\min}=-g/a^2\) tends to zero, this nonpolynomial oscillator reduces to a harmonic oscillator.


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Copyright information

© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratorio de Información Cuántica, CIDETECInstituto Politécnico Nacional, UPALM, CDMXMexico CityMexico
  2. 2.Catedrática CONACYT, CICInstituto Politécnico NacionalMexico CityMexico
  3. 3.Department of Mathematics and StatisticsUniversity of Prince Edward IslandCharlottetownCanada

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