Variational Monte Carlo (VMC) method and quantum well system in an external electric field VMC algorithm implementation and a study of wave function, energy and particle confinement at the ground state - Alinea, Allan L.
In this work, a quantum well system in a constant external electric field is considered. The potential distribution is such that the electric field range is localized and the potential is constant outside of the region of the field. A Variational Monte Carlo (VMC) implementation is developed for this potential distribution that is adaptable in small and large spatial field extent in solving for ground state energy and wave function. The results of the VMC calculation for energy calculations is compared with that of a method utilizing Airy functions in the small spatial field extent case. An excellent agreement is found in the comparison. Because of the structure of the potential distribution having a localized field effect, the confinement of the particle at the well exhibits interesting behavior. VMC calculation shows that a confinement at the well essentially remains constant for some field range, then drops off abruptly at a small field range and remains at constant small value near to zero for large field values. The confinement is found out to approximate a step function though it is argued that it is not a step function of field strength but just approximately behaving as such. From this behavior arises an interest for a maximum field strength before a certain confinement is overridden due to an increasing field. It is argued in this work that under some conditions, this maximum field strength has a linear dependency with potential depth.