FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2000, VOLUME 6, NUMBER 1, PAGES 311-314

**The confluent Heun equation with two singularities and
the modified Schrödinger equation with two accessory
parameters**

V. F. Tarasov

Abstract

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```
In this article we establish a connection
between the confluent Heun equation
(with two singularities $0$ and $\infty$) and the Schr\"odinger
equation for the hydrogen atom with two accessory parameters
$\mu$ and $\nu$, which ``influence'' the spectrum of eigenvalues
and the Coulomb potential.
```

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Last modified: April 11, 2000