Abstract. In a preceding paper (here referred as I) [1], we have shown that infinitely negative potentials at large distances have finite ground state energy if use is made of complex wave functions. We revisit this work in the case of the − $|x|^n$ potentials. We first reconsider the ground state energies. Then we discuss the first excited state. Finally, for the $n = 4$ case, the 4 first levels are calculated, and compared to the results of Bender and Boettcher [2].

1. R.J. Lombard, S. Garidi and R. Mezhoud, Rom. J. Phys. 67, 104 (2022).
2. C.M. Bender and S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998).

Key words: Quantum mechanics, complex wave functions, asymptotically negative potentials.