Analytic solutions of the quantum twostate problem in terms of the double, bi and triconfluent Heun functions
Abstract
We derive five classes of quantum timedependent twostate models solvable in terms of the double confluent Heun functions, five other classes solvable in terms of the biconfluent Heun functions, and a class solvable in terms of the triconfluent Heun functions. These classes generalize all the known families of two or threeparametric models solvable in terms of the confluent hypergeometric functions to more general fourparametric classes involving threeparametric detuning modulation functions. The particular models derived describe different nonlinear (parabolic, cubic, sinh, cosh, etc.) levelsweeping or levelglancing processes, double or triplelevelcrossing processes, as well as periodically repeated resonanceglancing or resonancecrossing processes. We show that more classes can be derived using the equations obeyed by certain functions involving the derivatives of the confluent Heun functions. We present an example of such a class for each of the three discussed confluent Heun equations.
 Publication:

Journal of Contemporary Physics (Armenian Academy of Sciences)
 Pub Date:
 July 2015
 DOI:
 10.3103/S1068337215030019
 arXiv:
 arXiv:1412.1378
 Bibcode:
 2015JConP..50..211S
 Keywords:

 Quantum Physics
 EPrint:
 J. Contemp. Physics (Armenian Ac. Sci.) 50, 211226 (2015)