• Publications
  • Influence
New solutions of Heun general equation
We show that in four particular cases the derivative of the solution of Heun general equation can be expressed in terms of a solution to another Heun equation. Starting from this property, we use theExpand
  • 45
  • 4
  • PDF
Schrödinger potentials solvable in terms of the confluent Heun functions
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 potentialsExpand
  • 41
  • 4
A conditionally exactly solvable generalization of the inverse square root potential
Abstract We present a conditionally exactly solvable singular potential for the one-dimensional Schrodinger equation which involves the exactly solvable inverse square root potential. Each of the twoExpand
  • 19
  • 2
  • PDF
Fifteen classes of solutions of the quantum two-state problem in terms of the confluent Heun function
We derive 15 classes of time-dependent two-state models solvable in terms of the confluent Heun functions. These classes extend over all the known families of three- and two-parametric modelsExpand
  • 38
  • 1
  • PDF
Solutions of the bi-confluent Heun equation in terms of the Hermite functions
We construct an expansion of the solutions of the bi-confluent Heun equation in terms of the Hermite functions. The series is governed by a three-term recurrence relation between successiveExpand
  • 32
  • 1
  • PDF
Hypergeometric expansions of the solutions of the general Heun equation governed by two-term recurrence relations for expansion coefficients
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 fromExpand
  • 10
  • 1
Schrödinger potentials solvable in terms of the general Heun functions
Abstract We show that there exist 35 choices for the coordinate transformation each leading to a potential for which the stationary Schrodinger equation is exactly solvable in terms of the generalExpand
  • 34
  • PDF
Exact solution of the Schrödinger equation for a short-range exponential potential with inverse square root singularity
Abstract.We introduce an exactly integrable singular potential for which the solution of the one-dimensional stationary Schrödinger equation is written through irreducible linear combinations of theExpand
  • 14
  • PDF
...
1
2
3
4
5
...