Nota de FísicaPublicado
Ince�s Limits for Confluent and Double-Confluent Heun Equations
Dados da publicação
- Autores
- —
- Tipo
- Nota de Física
- Status
- Publicado
- Data de publicação
- 27/12/2005
- Descrição
- We find pairs of solutions to a differential equation which is obtained as a special limit of a generalized spheroidal wave equation (this is also known as confluent Heun equation). One solution in each pair is given by a series of hypergeometric functions and converges for any finite value of the independent variable $z$, while the other is given by a series of modified Bessel functions and converges for $|z|>|z_{0}|$, where $z_{0}$ denotes a regular singularity. For short, the preceding limit is called Ince's limit after Ince who have used the same procedure to get the Mathieu equations from the Whittaker-Hill ones. We find as well that, when $z_{0}$ tends to zero, the Ince limit of the generalized spheroidal wave equation turns out to be the Ince limit of a double-confluent Heun equation, for which solutions are provided. Finally, we show that the Schr\"odinger equation for inverse fourth and sixth-power potentials reduces to peculiar cases of the double-confluent Heun equation and its Ince's limit, respectively.
- Ano
- 2005
- Número
- CBPF-NF-021/05
- Vínculo com tese
- Não
- Vínculo com bolsa
- Não