304 citations · 948 across the 35 of their papers we have counts for
12 papers · 1 filter
Algebraic structure behind Odrzywołek's EML operator
Tomasz Stachowiak
The binary EML operator yields all (transcendental) elementary functions by recursive application, or a binary tree. The structure of the operator itself carries two distinct ingre…
Non-integrability of the Kepler and the two-body problem on the Heisenberg group
Tomasz Stachowiak, Andrzej J. Maciejewski
The analog of the Kepler system defined on the Heisenberg group introduced by Montgomery and Shanbrom in [Fields Inst. Commun., Vol. 73, Springer, New York, 2015, 319-342, arXiv:12…
Hypergeometric First Integrals of the Duffing and van der Pol Oscillators
Tomasz Stachowiak
The autonomous Duffing oscillator, and its van der Pol modification, are known to admit time-dependent first integrals for specific values of parameters. This corresponds to the ex…
An exactly solvable system from quantum optics
Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak
We investigate a generalisation of the Rabi system in the Bargmann-Fock representation. In this representation the eigenproblem of the considered quantum model is described by a sy…
Comment on "Solvability of the two-photon Rabi Hamiltonian"
Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak
An implicit formula for the spectrum of the two-photon Rabi model was presented by Travenec in Phys. Rev. A 85, 043805 (2012) in analogy to the method of Braak [Phys. Rev. Lett. 10…
Analytical method of spectra calculations in the Bargmann representation
Andrzej J. Maciejewski, Maria Przybylska, Tomasz Stachowiak
We formulate a universal method for solving an arbitrary quantum system which, in the Bargmann representation, is described by a system of linear equations with one independent var…