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Analytic solutions of the quantum two-state problem in terms of the double-, bi- and tri-confluent Heun functions
T. A. Shahverdyan, T. A. Ishkhanyan, A. E. Grigoryan +1
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…
The Appell hypergeometric expansions of the solutions of the general Heun equation
A. M. Ishkhanyan
Starting from the equation obeyed by the derivative, we construct several expansions of the solutions of the general Heun equation in terms of the Appell generalized hypergeometric…
Thirty five classes of solutions of the quantum time-dependent two-state problem in terms of the general Heun functions
A. M. Ishkhanyan, T. A. Shahverdyan, T. A. Ishkhanyan
We derive 35 five-parametric classes of the quantum time-dependent two-state models solvable in terms of the general Heun functions. Each of the classes is defined by a pair of gen…
Expansions of the solutions of the general Heun equation governed by two-term recurrence relations for coefficients
T. A. Ishkhanyan, T. A. Shahverdyan, A. M. Ishkhanyan
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…
Expansions of the solutions to the confluent Heun equation in terms of the Kummer confluent hypergeometric functions
T. A. Ishkhanyan, A. M. Ishkhanyan
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…
Time-dependent level crossing models solvable in terms of the confluent Heun functions
A. M. Ishkhanyan, A. E. Grigoryan
We discuss the level-crossing field configurations for which the quantum time-dependent two-state problem is solvable in terms of the confluent Heun functions. We show that these c…