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

The present paper proposes an advancement beyond the recent mathematical formulation [Cherroud O and Yahiaoui S-A 2023 Eur. Phys. J. Plus. 138 534], by extending their approach to the evaluation of off-diagonal matrix elements 〈 x ˆ m p ˆ l 〉 n , n ′ J , J ′ for the 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 ˆ s 〉 n , n ′ J , J ′ and 〈 p ˆ 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 .