## 39 Citations

### SERIES SOLUTIONS OF CONFLUENT HEUN EQUATIONS IN TERMS OF INCOMPLETE GAMMA-FUNCTIONS

- MathematicsJournal of Applied Analysis & Computation
- 2019

We present a simple systematic algorithm for construction of expansions of the solutions of ordinary differential equations with rational coefficients in terms of mathematical functions having…

### Expansions of the Solutions of the General Heun Equation Governed by Two-Term Recurrence Relations for Coefficients

- MathematicsAdvances in High Energy Physics
- 2018

We examine the expansions of the solutions of the general Heun equation in terms of the Gauss hypergeometric functions. We present several expansions using functions, the forms of which differ from…

### A Conditionally Integrable Bi-confluent Heun Potential Involving Inverse Square Root and Centrifugal Barrier Terms

- Mathematics
- 2017

Abstract We present a conditionally integrable potential, belonging to the bi-confluent Heun class, for which the Schrödinger equation is solved in terms of the confluent hypergeometric functions.…

### Exact solutions of the sextic oscillator from the bi-confluent Heun equation

- PhysicsModern Physics Letters A
- 2019

In this paper, the sextic oscillator is discussed as a potential obtained from the bi-confluent Heun equation after a suitable variable transformation. Following earlier results, the solutions of…

### PT-Symmetric Potentials from the Confluent Heun Equation

- PhysicsEntropy
- 2021

The results are instructive in identifying which potentials can be obtained from this equation and under which conditions they exhibit PT symmetry, either unbroken or broken.

### Hermite function solutions of the Schrödinger equation for the sextic oscillator

- Physics, MathematicsPhysica Scripta
- 2020

We examine the conditions under which the solution of the radial stationary Schrödinger equation for the sextic anharmonic oscillator can be expanded in terms of Hermite functions. We find that this…

### A note on the generalized-hypergeometric solutions of general and single-confluent Heun equations

- MathematicsJournal of Mathematical Analysis and Applications
- 2021

### The second Exton potential for the Schrödinger equation

- PhysicsModern Physics Letters A
- 2019

Analytical solutions of the Schrödinger equation with a singular, fractional-power potential, referred to as the second Exton potential, are derived and analyzed. The potential is defined on the…

### A conditionally integrable Schrödinger potential of a bi-confluent Heun class

- Mathematics
- 2018

We present a bi-confluent Heun potential for the Schrödinger equation involving inverse fractional powers and a repulsive centrifugal-barrier term the strength of which is fixed to a constant. This…

## References

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### Exact solution of the Schrödinger equation for the inverse square root potential

- Mathematics
- 2015

We present the exact solution of the stationary Schrödinger equation for the potential . Each of the two fundamental solutions that compose the general solution of the problem is given by a…

### Expansions of the solutions to the confluent Heun equation in terms of the Kummer confluent hypergeometric functions

- Mathematics
- 2014

We examine the series expansions of the solutions of the confluent Heun equation in terms of three different sets of the Kummer confluent hypergeometric functions. The coefficients of the expansions…

### Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions

- Mathematics
- 2015

We construct several expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta functions and the Appell generalized hypergeometric functions of two variables of the…

### Integral equations for special functions of Heun class

- Mathematics
- 1996

Abstract. Integral equations equivalent to boundary problems for the diﬀeren-tial equations of Heun class are studied. A new method of their derivation isproposed which is not as general as the known…

### Schrödinger potentials solvable in terms of the confluent Heun functions

- Mathematics, Physics
- 2016

We show that if the potential is proportional to an energy-independent continuous parameter, then there exist 15 choices for the coordinate transformation that provide energy-independent potentials…

### Analytic solutions of the quantum two-state problem in terms of the double, bi- and triconfluent Heun functions

- Mathematics, Physics
- 2014

We derive five classes of quantum time-dependent two-state models solvable in terms of the double confluent Heun functions, five other classes solvable in terms of the biconfluent Heun functions, and…

### The Lambert-W step-potential – an exactly solvable confluent hypergeometric potential

- Mathematics, Physics
- 2016

### LETTER TO THE EDITOR: Analytic treatment of the polariton problem for a smooth interface

- Mathematics, Physics
- 2001

We study the polariton problem for smooth boundaries, i.e. whether or not there exist some localized solutions of Maxwell’s equations for different types of smooth spatial variation of complex…

### Discretization of Natanzon potentials

- Mathematics
- 2016

Abstract.We show that the Natanzon family of potentials is necessarily dropped into a restricted set of distinct potentials involving a fewer number of independent parameters if the potential term in…