Higher-order phase-space moments for off-diagonal rotating Morse oscillators

Abstract

The present paper proposes an advancement beyond the recent mathematical formulation [Cherroud and Yahiaoui 2023 Eur. Phys. J. Plus. 138, 534], by extending their approach to the evaluation of off-diagonal matrix elements 〈x ̂^m p ̂^l 〉_(n,n')^(J,J') for rotation-vibration Morse oscillators. Calculations are conducted within the framework of phase-space quantum mechanics, considering (〖r→r〗_eq). This methodology facilitates the derivation of analytical expressions for 〈x ̂^s 〉_(n,n')^(J,J') and 〈p ̂^s 〉_(n,n')^(J,J') matrix elements, where s = 1, 2, ..... This approach enables the evaluation of both diagonal (n = n',J = J' ≠ 0) and off-diagonal (n≠ n^',J = J^'≠ 0) matrix elements through a more explicit and compact analytic formula, applicable for cases where J≠ J' as well as for scenarios involving non-rotating effects J = J' = 0.