Solvable Analogue of V(x)=ix3
Abstract
Motivated by the recent doubts concerning the compatibility of the purely imaginary one-dimensional cubic-oscillator model with the standard postulates of quantum mechanics, we propose to replace its potential V(x)=ix3 by an elementary piece-wise constant function. We prove that such a simplified non-Hermitian model with a purely imaginary interaction potential still possesses infinitely many bound states with real energies. These states are shown to coincide, incidentally, with their Hermitian square-well analogues in the strong-coupling limit.
Fields of Study & Subjects
Algebraic and Geometric Analysis
Experimental and Theoretical Physics Studies
Publication details
- Journal / source
- Mathematics
- Publisher
- MDPI AG
- Volume
- 14
- Issue
- 3
- Pages
- 480–480
- Publication date
- 29 January 2026
- Language
- EN