article · AppliedMath
An investigation of a quantum system governed by an Eckart-like potential model provides exact analytical expressions for energy eigenvalues by solving the radial Schrödinger equation using the Greene-Aldrich approximation. By explicitly including the rotational quantum number, the ro-vibrational partition function is derived to determine vital thermodynamic functions such as Gibbs free energy, entropy, and enthalpy. Numerical evaluations indicate that the partition function increases continuously with temperature, Gibbs free energy declines as anticipated by statistical thermodynamics, entropy levels off at elevated temperatures, and enthalpy shows convex growth with added thermal energy. Parametric analysis establishes that adjusting potential characteristics, including screening parameters, permits the controlled manipulation of thermodynamic properties. The resulting formulations generalise earlier models, recover the Hulthén potential in limiting scenarios, and advance the theoretical comprehension of ro-vibrational statistical mechanics in exponential-type potentials.
Understanding the thermodynamic behaviour of molecular systems requires accurate mathematical models that incorporate both rotational and vibrational energy states. By providing closed-form solutions for an Eckart-like potential, this theoretical framework enhances the precision of statistical thermodynamic calculations, offering clearer insights into how thermal energy influences molecular stability, entropy, and heat capacity under varied physical conditions.
The abstract does not indicate an application pathway.
AI-generated from the published abstract. Always read the original work before citing.
This study obtained the energy levels and examined the partition function (Z) of a quantum system described by an Eckart-like potential model. By adopting the Greene–Aldrich approximation scheme for the centrifugal term, the radial Schrödinger equation (SE) is solved and the analytic expression of the energy eigenvalues is obtained. The ro-vibrational Z is computed by explicitly incorporating the rotational quantum number, a feature often neglected or misapplied in many studies. This result is used to evaluate the key thermodynamic properties (TP), including the Gibbs free energy (G), entropy (S), and enthalpy (H). Numerical analysis reveals that the Z increases monotonically with temperature, while the G decreases in accordance with statistical thermodynamics. The S exhibits saturation-like behaviour at higher temperatures, while the H displays convex growth with increasing thermal energy. Parametric studies demonstrate that the Eckart-like potential allows for the controlled tuning of TP, with variations in the potential parameters, including the screening parameter, having distinct effects. The results generalise existing models, reproduce the Hulthén potential under specific conditions, show the effect of the rotational quantum number of TP, and provide new insights into the ro-vibrational statistical mechanics of exponential-type potentials.
This page summarises published work. The authoritative version sits with the publisher.
DOI: 10.3390/appliedmath6080130
Is something wrong with this record? Report it or request removal.
Discussion
Have you built on this work, tried to replicate it, or seen it applied in practice? Share what you know. Verified researchers and MARATTO™ domain experts can open a discussion, and any member can reply. Contributions are reviewed before they appear.
No discussion yet. Open the first thread.
New to MARATTO™? Create a free account.
