Series solutions of ${\mathscr{P}}{\mathscr{T}}$-symmetric Schrödinger equations
Carl M. BenderDepartment of Physics, Washington University, St. Louis, Missouri 63130, United States of AmericaC FordDepartment of Mathematics, Imperial College London, London SW7 2AZ, United KingdomNima HassanpourDepartment of Physics, Washington University, St. Louis, Missouri 63130, United States of AmericaB XiaDepartment of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
2018en
ABI
Abstract
A simple and accurate numerical technique for finding eigenvalues, node structure, and expectation values of -symmetric potentials is devised. The approach involves expanding the solution to the Schrdinger equation in series involving powers of both the coordinate and the energy. The technique is designed to allow one to impose boundary conditions in -symmetric pairs of Stokes sectors. The method is illustrated by using many examples of -symmetric potentials in both the unbroken-and broken- -symmetric regions.
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