In this paper, the formalism of improved quantization rule is used to obtain analytical expression for bound state ro-vibrational energies of the improved Pschl–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 Pschl–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.

在本文中，改进的量化规则的形式用于获得改进的Pschl-Teller振荡器（IPTO）的束缚态旋转振动能的解析表达式。在模拟有效势的离心项时，使用了类 Pekeris 近似方案。解析归一化特征函数的表达式是通过 ansatz 求解技术获得的。然后使用获得的旋转振动能量方程来推导出 IPTO 一些重要热力学函数的关系；这些包括 ro-vibrational：分配函数、亥姆霍兹自由能、平均能量、熵和比热容。使用 RbH (X ¹ Σ⁺ ) 双原子分子，计算 IPTO 的纯振动态能量。获得的结果与实验 Rydberg-Klein-Rees 数据非常一致，并且优于通过改进的广义 Pschl-Teller 势获得的 RbH (X ¹ Σ ⁺ ) 双原子分子的能量。研究还表明，旋转振动分配函数随着温度 ( T ) 或上限振动量子数 ( λ ) 的增加而单调增加。另一方面，任何T或λ 的增加都会导致系统的旋转振动亥姆霍兹自由能单调减少。