A class of spherically-separable non-Hermitian PphiTphi-symmetric Hamiltonians

TL;DR

This paper investigates a family of spherical non-Hermitian potentials with a novel PφTφ-symmetry, revealing that while eigenvalues mirror those of V(r), the wavefunctions exhibit new probabilistic interpretations due to azimuthal modifications.

Contribution

It introduces a new class of PφTφ-symmetric non-Hermitian Hamiltonians with unique wavefunction properties and probabilistic interpretations.

Findings

Eigenvalues match those of the potential V(r)

Wavefunctions have altered probabilistic interpretations

New PφTφ-symmetry observed in spherical non-Hermitian systems

Abstract

A family of spherical non-Hermitian potentials is studied. It is shown that the corresponding non-Hermitian Hamiltonians admit some "new" P$phi$T$phi$-symmetry. It is observed that whilst such P$phi$T$phi$-symmetric Hamiltonians just copy the eigenvalues of V(r), the corresponding wavefunctions would rather indulge some new probabilistic interpretations due to the change in the azimuthal part.