PT-symmetry rules applied to a class of real potentials

Abstract

Extending the functional space to complex eigenfunctions R J Lombard et al (2022, Rom. J. Phys.67, 104), we have shown that infinitely negative potentials at large distances admit finite energy states. The used techniques are similar to the ones applied in the case of PT symmetric complex potentials with real eigenvalues. We present the lowest part of the spectra for −∣x∣n potentials with 4 ≤ n ≤ 8. We also discuss the norm and orthogonality of the wave functions.