Quantum dynamics in confined pseudo-harmonic oscillator in a time-dependent moving

TL;DR

This paper provides an analytical solution to the Schrödinger equation for a confined pseudoharmonic oscillator with a moving boundary, exploring quantum dynamics, uncertainties, and molecular properties in a time-dependent setting.

Contribution

It is the first detailed analysis of a non-harmonic potential with a time-dependent moving boundary, including solutions for energy, force, pressure, and molecular correlation functions.

Findings

Minimum uncertainty product remains above h/2

Time-dependent energy and force expressions derived

Time correlation functions depend on internuclear distance ratio

Abstract

In this work, we present analytical solution of Schr\"odinger equation of confined pseudoharmonic potential in presence of a moving boundary condition, for an arbitrary angular momentum state. It turns out that an important quantity to probe the problem is internuclear distance ratio, which depends on the solution of Ermakov equation. The minimum value of time-dependent (TD) Heisenberg uncertainty product always remains greater than that of the minimum uncertainty product h/2. The TD average energy is derived analytically in a closed form and the corresponding average force and average pressure are defined. Moreover, time correlation function of two states for the case of six selected diatomic molecules (CO, NO, ScH, CH, H2, N2) is obtained. It is found to depend on internuclear distance ratio at two different time domains. The TD survival probability and average life-time of molecule in a confined quantum system are defined. Expressions are offered for quantum similarity measure, dissimilarity and quantum similarity index. The latter is given for a pair of molecules. The obtained results are compared with available literature, wherever possible. To our knowledge this is the first detailed report of a non-harmonic central potential in a TD moving boundary condition.