Work

Isochronous oscillator with a singular position-dependent mass and its quantization

Year: 2025

Type: article

Abstract: In this paper, we present an analysis of the equation ẍ−(1/2x)ẋ2+2ω2x−1/8x=0, where ω > 0 and x = x(t) is a real-valued variable. We first discuss the appearance of this equation from a position-dependent-mass scenario in which the mass profile goes inversely with x, admitting a singularity at x = 0. The associated potential is also singular at x = 0, splitting the real axis into two halves, i.e., x > 0 and x < 0. The dynamics is exactly solvable for both the branches and so for definiteness, we stick to the x > 0 branch. Performing a canonical quantization in the position representation and upon employing the ordering strategy of the kinetic-energy operator due to von Roos, we show that the problem is isospectral to the isotonic oscillator. Thus, the quantum spectrum consists of an infinite number of equispaced levels. The spacing between the energy levels is found to be insensitive to the specific choices of the ambiguity parameters that are employed for ordering the kinetic-energy operator à la von Roos.

Source: Journal of Mathematical Physics

DOI: 10.1063/5.0271167

Authors: Aritra Ghosh, Bhabani Prasad Mandal, Bijan Bagchi

Institutions: Rochester Institute of Technology, Indian Institute of Technology Bhubaneswar, Banaras Hindu University, University of Calcutta

Language: English

Topic: Quantum Mechanics and Non-Hermitian Physics

Subfield: Atomic and Molecular Physics, and Optics

Field: Physics and Astronomy

Domain: Physical Sciences

Open Access status: green

Funders: Banaras Hindu University, Ministry of Education, India

Awards: G4262413115, G4721328195, G5612045768, G906842842