Series Solutions of PT-Symmetric Schr\"odinger Equations

TL;DR

This paper develops a series solution method for PT-symmetric Schrödinger equations with Bender-Boettcher potentials, providing accurate energy levels and state properties for various N through simple truncation.

Contribution

It introduces a straightforward truncation approach to solve PT-symmetric Schrödinger equations with Bender-Boettcher potentials, enabling precise computation of energy states.

Findings

Accurate energy levels for ground and excited states across N values.

Explicit computation of node structures and expectation values.

Validation of the method through numerical examples.

Abstract

We consider series solutions of the Schr\"odinger equation for the Bender-Boettcher potentials V(x)=-(ix)^N with integer N. A simple truncation is introduced which provides accurate results regarding the ground state and first few excited states for any N. This is illustrated with explicit computations of energy levels, node structure and expectation values for some integer N.