# Calculation of eigenvalues by Greens-functions and the Lippmann-Schwinger equation

## TL;DR

This paper presents a numerical method using the Lippmann-Schwinger equation to accurately compute eigenvalues of one-dimensional quantum systems, demonstrating its application to various potentials and eigenvalue engineering.

## Contribution

It introduces a novel numerical approach for calculating quantum eigenvalues via the Lippmann-Schwinger equation, applicable to diverse potential types and eigenvalue manipulation.

## Key findings

- Successfully computed eigenvalues for multiple potential types
- Demonstrated eigenvalue-engineering capabilities
- Validated method against known quantum systems

## Abstract

We calculate eigenvalues of one-dimensional quantum-systems by the exact numerical solution of the Lippmann-Schwinger equation, analogous to the scattering problem. To illustrate our method, we treat elementary problems: the harmonic and quartic oscillator, a symmetric and a skew double-well potential, and potentials with finite and infinite depth. Furthermore, we show how our method can be used for eigenvalue-engineering.