Exact solvability of potentials with spatially dependent effective masses

Remarks on exact solvability of quantum systems with spatially varying effective mass

Within the frame of a novel treatment we make a complete mathematical analysis of exactly solvable one-dimensional quantum systems with non-constant mass, involving their ordering ambiguities. This work extends the results recently reported in the literature and clarifies the relation between physically acceptable effective mass Hamiltonians.

When can gravity path-entangle two spatially superposed masses?

An experimental test of quantum effects in gravity has recently been proposed, where the ability of the gravitational field to entangle two masses is used as a witness of its quantum nature. The key idea is that if gravity can generate entanglement between two masses then it must have at least some quantum features (i.e., two non-commuting observables). Here we discuss what existing models for coupled matter and gravity predict for this experiment. Collapse-type models, and also quantum field theory in curved spacetime, as well as various induced gravities, do not predict entanglement generati…

Supersymmetric approach to exactly solvable systems with position-dependent effective masses

We discuss the relationship between exact solvability of the Schrödinger equation with a position-dependent mass and the ordering ambiguity in the Hamiltonian operator within the frame of supersymmetric quantum mechanics. The one-dimensional Schrödinger equation, derived from the general form of the effective mass Hamiltonian, is solved exactly for a system with exponentially changing mass in the presence of a potential with similar behaviour, and the corresponding supersymmetric partner Hamiltonians are related to the effective-mass Hamiltonians proposed in the literature.

Three-body problem in $d$-dimensional space: ground state, (quasi)-exact-solvability

As a straightforward generalization and extension of our previous paper, J. Phys. A50 (2017) 215201 we study aspects of the quantum and classical dynamics of a $3$-body system with equal masses, each body with $d$ degrees of freedom, with interaction depending only on mutual (relative) distances. The study is restricted to solutions in the space of relative motion which are functions of mutual (relative) distances only. It is shown that the ground state (and some other states) in the quantum case and the planar trajectories (which are in the interaction plane) in the classical case are of this…

An alternative approach to Schrödinger equations with a spatially varying mass

Extending the point canonical transformation approach in a manner distinct from the previous ones, we propose a unified approach of generating potentials of all classes having non-constant masses.

三量子比特量子引力诱导质量纠缠（QGEM）中三体纠缠的演化

Evolution of tripartite entanglement in three-qubit Quantum Gravity-Induced Entanglement of Masses (QGEM) with quantum decoherence

研究三量子比特QGEM实验中 decoherence 的影响，分析三体纠缠的生成与检测方法。