Fifteen classes of solutions of the quantum two-state problem in terms of the confluent Heun function

DOI10.1088/1751-8113/47/46/465205zbMath1307.81081arXiv1402.1326OpenAlexW3098110348MaRDI QIDQ2936417

A. E. Grigoryan, A. M. Ishkhanyan

Publication date: 16 December 2014

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1402.1326

zbMATH Keywords

analytic solutionsconfluent Heun functionquantum two-state problem

Mathematics Subject Classification ID

Quantum optics (81V80) Lasers, masers, optical bistability, nonlinear optics (78A60) Special functions in characteristic (p) (gamma functions, etc.) (33E50) Confluent hypergeometric functions, Whittaker functions, ({}_1F_1) (33C15) Special quantum systems, such as solvable systems (81Q80)

Related Items (16)

A conditionally exactly solvable generalization of the inverse square root potential ⋮ Expansions of the solutions of the general Heun equation governed by two-term recurrence relations for coefficients ⋮ Integral relations for solutions of the confluent Heun equation ⋮ Schrödinger potentials solvable in terms of the confluent Heun functions ⋮ The Lambert-\(W\) step-potential -- an exactly solvable confluent hypergeometric potential ⋮ Solving eigenproblem by duality transform ⋮ Solutions of the bi-confluent Heun equation in terms of the Hermite functions ⋮ Analytical results for a spin–orbit coupled atom held in a non-Hermitian double well under synchronous combined modulations ⋮ Generating arbitrary analytically solvable two-level systems ⋮ Schrödinger potentials solvable in terms of the general Heun functions ⋮ Convergence and applications of some solutions of the confluent Heun equation ⋮ Four five-parametric and five four-parametric independent confluent Heun potentials for the stationary Klein-Gordon equation ⋮ Expansions of the solutions of the confluent Heun equation in terms of the incomplete Beta and the Appell generalized hypergeometric functions ⋮ Generalized confluent hypergeometric solutions of the Heun confluent equation ⋮ Floquet theory of the analytical solution of a periodically driven two-level system ⋮ γ-rigid version of Bohr Hamiltonian with the modified Davidson potential in the position-dependent mass formalism

This page was built for publication: Fifteen classes of solutions of the quantum two-state problem in terms of the confluent Heun function