TL;DR
This paper introduces a pseudo time formulation of quantum mechanics derived from reparametrisation of time in Hamiltonian path integrals, linking it to supersymmetric quantum mechanics and key concepts like shape invariance.
Contribution
It presents a novel pseudo time operator formalism in quantum mechanics, connecting reparametrisation of time with supersymmetry and spectral deformation techniques.
Findings
Pseudo time formalism relates to supersymmetric quantum mechanics
Shape invariance appears naturally in pseudo time quantum mechanics
Isospectral deformation is incorporated into the framework
Abstract
Based on some results on reparmetrisation of time in Hamiltonian path integral formalism, a pseudo time formulation of operator formalism of quantum mechanics is presented. Relation of reparametrisation of time in quantum with super symmetric quantum mechanics is established. We show how some important concepts such as shape invariance and tools like isospectral deformation appear in pseudo time quantum mechanics.
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Taxonomy
TopicsQuantum Mechanics and Non-Hermitian Physics · Quantum chaos and dynamical systems · Noncommutative and Quantum Gravity Theories