Exact solutions of an asymmetric double well potential

Guo Hua Sun, Qian Dong, V. B. Bezerra, Shi Hai Dong

Research output: Contribution to journalArticlepeer-review

Abstract

The analytical solutions of an asymmetric double well potential V(x)=ax2-bx3+cx4 are found to be a triconfluent Heun function HT(α, β, γ; z). It should be emphasized that these potential parameters are taken arbitrarily without any restriction on them. The wave functions which depend on the potential parameters are shrunk toward to the origin for given b and c when the parameter a increases, while they are moved far from the origin and toward to the left when the parameter b increases for given a and c. Also, when the parameter c increases for given a and b they have the similar property to the case when the parameter a increases.

Original languageEnglish
JournalJournal of Mathematical Chemistry
DOIs
StateAccepted/In press - 2022

Keywords

  • Asymmetric double well potential
  • Exact solution
  • Triconfluent Heun differential equation

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