Average energy and quantum similarity of a time dependent quantum system subject to Pöschl–Teller potential

• Published in: Journal of mathematical chemistry Vol. 60; no. 2; pp. 1 - 21
• Main Authors: Carbó-Dorca, Ramon, Nath, Debraj
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.02.2022; Springer Nature B.V
• Subjects: Boundary conditions; Chemistry; Chemistry and Materials Science; Dependent variables; Diatomic molecules; Exact solutions; Math. Applications in Chemistry; Original Paper; Physical Chemistry; Quantum theory; Schrodinger equation; Similarity; Theoretical and Computational Chemistry; Time dependence; Time-dependent Schrödinger equation; Pöschl–Teller potential; Rovibrational energy; Quantum similarity index; Average energy
• ISSN: 0259-9791; 1572-8897
• DOI: 10.1007/s10910-021-01318-3

Exact solutions of time-dependent Schrödinger equation in presence of generalized Pöschl–Teller like potential plus oscillator potential are defined analytically with help of point transformation and separation of variables. The time-dependent average energy is expressed in terms of a dimensionless scale factor L of a quantum state with a time-dependent moving boundary condition. Moreover, quantum similarity measures and indices between two states are defined. Numerical values of rovibrational energy in presence and absence of centrifugal term, and average energy in absence of centrifugal term have been calculated for ten selected diatomic molecules: { H 2 , LiH, HF, HCl, N 2 , CO, SiO, O 2 , F 2 , NO}. In addition, the quantum similarity index between pairs of these selected molecules is calculated.