Thermodynamic relations and ro-vibrational energy levels of the improved Pöschl–Teller oscillator for diatomic molecules

In this paper, the formalism of improved quantization rule is used to obtain analytical expression for bound state ro-vibrational energies of the improved Pöschl–Teller oscillator (IPTO). In modeling the centrifugal term of the effective potential, a Pekeris-like approximation scheme is used. Expression for analytical normalized eigenfunctions is obtained by ansatz solution technique. The equation obtained for ro-vibrational energy is then used to derive relations for some important thermodynamic functions for the IPTO; these include ro-vibrational: partition function, Helmholtz free energy, mean energy, entropy and specific heat capacity. Using the spectroscopic data of RbH (X1Σ+) diatomic molecule, pure vibrational state energies for the IPTO are calculated. The results obtained are in good agreement with experimental Rydberg–Klein–Rees data and are better than energies of the RbH (X1Σ+) diatomic molecule obtained via improved generalized Pöschl–Teller potential. Studies have also shown that the ro-vibrational partition function increases monotonically with increase in either temperature (T) or upper bound vibrational quantum number (λ). On the other hand, increase in any of T or λ results in monotonic decrease in ro-vibrational Helmholtz free energy of the system.