Quantum solvability of a nonlinear δ-type mass profile system: coupling constant quantization

In this paper, we discuss the quantum dynamics of a nonlinear system that admits temporally localized solutions at the classical level. We consider a general ordered position-dependent mass Hamiltonian in which the ordering parameters of the mass term are treated as arbitrary. The mass function here is singular at the origin. We observe that the quantum system admits bounded solutions but importantly the coupling parameter of the system gets quantized which has also been confirmed by the semiclassical study as well.

Automated summary

In this paper, we discuss the quantum dynamics of a nonlinear system that has temporally localized solutions at the classical level. We consider a general ordered position-dependent mass Hamiltonian with arbitrary ordering parameters for the mass term. The mass function in this case is singular at the origin. We observe that the quantum system has bounded solutions, but the coupling parameter of the system becomes quantized, which is also confirmed by semiclassical study.