Some Special Solutions of Biconfluent and Triconfluent Heun Equations in Elementary Functions by Extended Nikiforov–Uvarov Method

We report some special solutions of biconfluent Heun equation and triconfluent Heun equation via extended Nikiforov–Uvarov (NU) method which is developed by changing the boundary conditions of NU method [8]. We demonstrate that eigenvalue solutions of these confluent forms of Heun equation can be ac...

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Bibliographic Details
Published in:Reports on mathematical physics 2015-12, Vol.76 (3), p.271-281
Main Authors: Karayer, H., Demirhan, D., Büyükkiliç, F.
Format: Article
Language:English
Subjects:
biconfluent Heun equation
extended Nikiforov–Uvarov method
triconfluent Heun equation
two-electron quantum dot model problem
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Summary:We report some special solutions of biconfluent Heun equation and triconfluent Heun equation via extended Nikiforov–Uvarov (NU) method which is developed by changing the boundary conditions of NU method [8]. We demonstrate that eigenvalue solutions of these confluent forms of Heun equation can be achieved exactly. Furthermore we give eigenvalue solution of a two-electron quantum dot model problem as a physical application of extended NU method.
ISSN:0034-4877
1879-0674
DOI:10.1016/S0034-4877(15)00039-7