The thermodynamic property for the particle confined in a linear potential

• Published in: Chemical physics 2023-01, Vol.565, p.111734, Article 111734
• Main Authors: Wang, De-hua, Liu, Xue, Xie, Xin-yu, Liu, Wei, Chu, Bin-hua, Zhao, Gang
• Format: Article
• Language: English
• Subjects: Linear potential; Quantum confinement; Thermodynamic property
• ISSN: 0301-0104
• DOI: 10.1016/j.chemphys.2022.111734

We study the quantum confinement effects on the thermodynamic property for the particle confined in a linear potential. The energy eigen-values and eigen wave functions of the particle subjected to a spatial confinement by a linear potential have been derived by solving the Schrodinger equation. Our calculation results show that the thermodynamic properties of this system, such as the average energy, the heat capacity and the chemical potential depend sensitively on the width of the quantum well and the gradient of the linear potential. For instance, in the heat capacity curve of the confined particle as a function of the thermodynamic temperature, there exist different regions. For smaller size of the quantum well, the quantum confinement effect on the particle becomes significant in comparison to the effect of the linear potential, the heat capacity curve of the current system approaches to the case of the particle in the one-dimensional (1-D) infinitely deep quantum well. For larger size of the quantum well, the effect of the linear potential plays an important role. In the low temperature region, the heat capacity curve is close to the particle in the linear potential confined in the half space, and the quantum confinement only affect the heat capacity at high temperature region. These results suggest that the thermodynamic property for the particle confined in a linear potential exhibits a phase transition modified by the width of the quantum well and the thermodynamic temperature. Our work provides some references for the experimental research on the thermodynamic property of the confined particle and has some practical applications in statistical physics, chemical physics, ion trap, etc.