Quantum Isothermal Reversible Process of Particles in a Box with a Delta Potential

TL;DR

This paper investigates a quantum heat engine with a particle in a box featuring a delta potential, analyzing how quantum tunneling affects the reversible work during isothermal expansion.

Contribution

It provides a quantum mechanical analysis of an isothermal reversible process in a particle-in-a-box system with a delta potential, including energy levels and thermodynamic potentials.

Findings

Quantum tunneling reduces reversible work output.

Energy levels are affected by the delta potential.

Thermodynamic potentials are derived from Schrödinger equation.

Abstract

For an understanding of a heat engine working in the microscopic scale, it is often necessary to estimate the amount of reversible work extracted by isothermal expansion of the quantum gas used as its working substance. We consider an engine with a movable wall, modeled as an infinite square well with a delta peak inside. By solving the resulting one-dimensional Schr\"odinger equation, we obtain the energy levels and the thermodynamic potentials. Our result shows how quantum tunneling degrades the engine by decreasing the amount of reversible work during the isothermal expansion.