Bootstrapping PT symmetric Hamiltonians

TL;DR

This paper extends the bootstrap method to PT symmetric non-Hermitian Hamiltonians by defining a new positivity condition, enabling the derivation of their eigenspectrum through illustrative examples.

Contribution

It introduces a modified positivity condition tailored for PT symmetric Hamiltonians, expanding the bootstrap approach to non-Hermitian quantum systems.

Findings

Successfully derived eigenspectra for PT symmetric Hamiltonians

Demonstrated the modified positivity condition with multiple examples

Extended bootstrap techniques to non-Hermitian systems

Abstract

Bootstrapping in Quantum Mechanics uses positivity condition to derive the Eigenspectum. For non-hermitian systems usual positivity condition does not work. In this paper we define positivity condition for special class of non-hermitian hamiltonian, the PT symmetric Hamiltonian. We illustrate this modified positivity condition with several examples and obtain eigenspectrum.