Thermodynamic properties of a GaAs quantum well from semi-relativistic quantum mechanics

A semi-relativistic quantum mechanical equation is arrived at. This is achieved by considering the Taylor series expansion of the energy of a particle to the fourth, sixth order and later generalized to infinity. As an illustration of the equations obtained herein, thermodynamic properties of a GaAs quantum well are evaluated. The results obtained considering the fourth and sixth order contributions are compared with those obtained from the second order Schrodinger equation. The contributions of the fourth and sixth order corrections are studied under different conditions. Results show that fourth order contributions are more significant than those of the sixth order, particularly for narrow quantum wells.