The quantum engine cycle serves as an analogous representation of classical
heat engines for microscopic systems and the quantum regime of thermal devices
is composed of a single element. In this work, the Quantum-Mechanical
properties of a non-linear quantum oscillator described by the Woods-Saxon [WS]
model are examined. The Quantum-Mechanical analogue of the Carnot cycle was
constructed using changes in both the width L of the well and the quantum state
of the potential well. The efficiency of the quantum engine, consisting of
adiabatic and isothermal processes based on the Woods-Saxon [WS] potential is
derived. The result is shown to be analogous to that of the classical engine
and found to agree, within an appropriate limit, with existing results obtained
from other potential models. This implies that the [WS] potential can be used
as an alternative model in quantum engines.
