Quantum dual engine with working substance of a single particle inside the cubic potential

A dual engine with one particle in a three-dimensional symmetry potential well, as a quantum working fluid, has been modeled. This research is based on the possibility to enhance the efficiency of a classical dual engine based on the 1^st law of thermodynamics. The quantum system used is a modified analogy from the classical thermodynamic system, which is the ideal gas in the piston cylinder. By assuming the ideal gas pressure as a potential wall mechanical force, the ideal gas volume as the width of the potential well, and the ideal gas temperature as the total energy expectation value for a single particle, a dual quantum engine can be built theoretically. The five processes that work on each classical dual cycle can be analogous to the quantum system. The result is the similarity thermal efficiency equation of a quantum dual engine and the classical one. Besides, the heat capacity ratio of the quantum dual engine is greater than the classical engine which causes the efficiency of the quantum version to outperform the classical version when it is in the same mechanical ratio conditions.