scholarly journals Generalized Hypergeometric Solutions of the Heun Equation

2020 ◽  
Vol 202 (1) ◽  
pp. 1-10
Author(s):  
A. M. Ishkhanyan
Keyword(s):  
Heun Equation ◽  
Hypergeometric Solutions

scholarly journals The Rabi problem with elliptical polarization

2020 ◽  
Vol 75 (11) ◽  
pp. 937-962
Author(s):  
Heinz-Jürgen Schmidt
Keyword(s):  
Floquet Theory ◽  
Equation Of Motion ◽  
Quantum Spin ◽  
Heun Equation ◽  
Elliptical Polarization ◽  
Third Order ◽  
Polynomial Coefficients ◽  
Resonance Frequencies ◽  
Classical Quantum ◽  
Elliptically Polarized

AbstractWe consider the solution of the equation of motion of a classical/quantum spin subject to a monochromatical, elliptically polarized external field. The classical Rabi problem can be reduced to third-order differential equations with polynomial coefficients and hence solved in terms of power series in close analogy to the confluent Heun equation occurring for linear polarization. Application of Floquet theory yields physically interesting quantities like the quasienergy as a function of the problem’s parameters and expressions for the Bloch–Siegert shift of resonance frequencies. Various limit cases are thoroughly investigated.

The Heun Equation and the Darboux Transformation

2006 ◽  
Vol 79 (1-2) ◽  
pp. 244-253 ◽  
Author(s):  
Yu. N. Sirota ◽  
A. O. Smirnov
Keyword(s):  
Darboux Transformation ◽  
Heun Equation
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