Solutions of the bi-confluent Heun equation in terms of the Hermite functions

@article{Ishkhanyan2016SolutionsOT,
  title={Solutions of the bi-confluent Heun equation in terms of the Hermite functions},
  author={T. A. Ishkhanyan and Artur M. Ishkhanyan},
  journal={arXiv: Quantum Physics},
  year={2016}
}

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References

SHOWING 1-10 OF 62 REFERENCES

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

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

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

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

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

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

A conditionally exactly solvable generalization of the inverse square root potential

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

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

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

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

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
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