Scattering off PT-symmetric upside-down potentials

TL;DR

This paper proposes a macroscopic quantum scattering experiment to directly observe and measure the bound-state energies of PT-symmetric upside-down potentials, which have real spectra despite their unbounded nature.

Contribution

It introduces a novel experimental setup for observing bound states in PT-symmetric upside-down potentials, bridging theoretical predictions with practical measurement.

Findings

Bound states exist with real, positive energies in these potentials.

The proposed experiment enables direct measurement of these energies.

PT-symmetric boundary conditions lead to real spectra in unbounded potentials.

Abstract

The upside-down $-x^4$, $-x^6$, and $-x^8$ potentials with appropriate PT-symmetric boundary conditions have real, positive, and discrete quantum-mechanical spectra. This paper proposes a straightforward macroscopic quantum-mechanical scattering experiment in which one can observe and measure these bound-state energies directly.