Effect of Cyclotron Frequency on Vibrational Partition Function and Enthalpy for Hellmann Potential

Abstract

This study presents a comparative analysis of the eigenvalues, vibrational partition function, and vibrational enthalpy of the Hellmann potential under different quantum states, cyclotron frequencies, and temperatures. The study reveals that the eigenvalue at higher quantum states exhibit less negativity values, with the present method consistently yielding lower eigenvalues than the NU and AP methods. The effect of cyclotron frequency on eigenvalues indicates an upward energy shift with increasing frequency, while spacing between successive energy levels increases at higher quantum numbers. The vibrational partition function exhibits temperature-dependent behaviour, increasing steadily in some cases while showing fluctuations and saturation effects at specific values of cyclotron
frequency. Similarly, the vibrational enthalpy trends suggest stabilization at higher temperatures, with variations in magnitude and rate of change depending on cyclotron frequency. These findings highlight the complex interplay between quantum state, cyclotron frequency, and thermal effects on the Hellmann potential system.

Keywords: Bound state; Wave equation; Eigensolutions; Thermodynamic properties; Potential model.

2010 Mathematics Subject Classification. 26A25; 26A35