Exact solutions of the Schrödinger equation with a complex periodic potential

Determinantal varieties (14M12) Estimates of eigenvalues in context of PDEs (35P15) Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics (81Q05) Spectrum, resolvent (47A10) Applications of Lie groups to the sciences; explicit representations (22E70) Constrained dynamics, Dirac's theory of constraints (70H45) Time-dependent Schrödinger equations and Dirac equations (35Q41)

Cites Work

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A note on the \(\mathcal PT\) invariant periodic potential \(V(x) = 4\cos^2x + 4iV_0\sin2x\)
Tunneling times in complex potentials
The improved quantization rule and the Langer modification
Energy spectrum of the trigonometric Rosen-Morse potential using an improved quantization rule
Analytic solutions in the dyon black hole with a cosmic string: scalar fields, Hawking radiation and energy flux
Semi-exact solutions of sextic potential plus a centrifugal term
Factorization method in quantum mechanics
Exact solutions of the Razavy cosine type potential
Semiexact solutions of the Razavy potential
Confluent Heun functions and the physics of black holes: resonant frequencies, Hawking radiation and scattering of scalar waves
Schrödinger potentials solvable in terms of the general Heun functions
Schrödinger operators with complex potential but real spectrum
Exact solutions of the 1D Schrödinger equation with the Mathieu potential
A new quantization rule to the bound state problem in non-relativistic quantum mechanics
New findings for two new type sine hyperbolic potentials
Exact solutions of the sine hyperbolic type potential
One-dimensional crystal with a complex periodic potential
Exact solutions to solitonic profile mass Schrödinger problem with a modified Pöschl–Teller potential
Wave Equations in Higher Dimensions
Semi-exact Solutions of Konwent Potential
Novel relations and new properties of confluent Heun's functions and their derivatives of arbitrary order
Exact solutions to the Schrödinger equation for the potential in two dimensions
Asymptotic iteration method for eigenvalue problems
Real Spectra in Non-Hermitian Hamiltonians Having<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="bold-script">P</mml:mi><mml:mi mathvariant="bold-script">T</mml:mi></mml:math>Symmetry
Heun functions and quasi-exactly solvable double-well potentials
Exact solutions of the harmonic oscillator plus non-polynomial interaction
Exact solutions of a quartic potential
On a solution of the Schrödinger equation with a hyperbolic double-well potential
A complex periodic QES potential and exceptional points
Energy band structure due to a complex, periodic, PT-invariant potential

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