Scattering amplitudes for the rationally extended P T symmetric complex potentials

Abstract

In this paper, we consider the rational extensions of two different P T symmetric complex potentials namely the asymptotically vanishing Scarf II and asymptotically non-vanishing Rosen-Morse II [ RM-II] potentials and obtain bound state eigenfunc- tions in terms of newly found exceptional Xm Jacobi polynomials and also some new type of orthogonal polynomials respectively. By considering the asymptotic behaviour of the exceptional polynomials, we obtain the reflection and transmission amplitudes for them and discuss the various novel properties of the corresponding amplitudes.

18 pages, Latex, No Figs

References in corpus (8)

• Making Sense of Non-Hermitian Hamiltonians
• Faster than Hermitian Quantum Mechanics
• Infinitely many shape invariant potentials and new orthogonal polynomials
• A note on the PT-invariant periodic potential V(x)=4 cos^2 x + 4 i V_0 sin 2x
• Parametric symmetries in exactly solvable real and P T symmetric complex potentials
• Group theoretic approach to rationally extended shape invariant potentials
• Exceptional points in quantum and classical dynamics
• Infinite families of (non)-Hermitian Hamiltonians associated with exceptional $X_m$ Jacobi polynomials

Cited by in corpus (8)

• Parametric symmetries in exactly solvable real and P T symmetric complex potentials
• New scattering features in non-Hermitian space fractional quantum mechanics
• A class of exactly solvable rationally extended non-central potentials in Two and Three Dimensions
• A class of exactly solvable rationally extended Calogero-Wolfes type 3-body problems
• Rationally extended many-body truncated Calogero-Sutherland model
• Supersymmetry and Shape Invariance of exceptional orthogonal polynomials
• Solutions of (1+1)-dimensional Dirac equation associated with exceptional orthogonal polynomials and the parametric symmetry
• Quantum phase transitions and entanglement entropy in a non-Hermitian Jaynes-Cummings model