تأثير معامل الازاحة المعمم على معامل النفاذية و الانعكاس للحواجز والآبار الكمومية

Abstract

In this work, we studied two physical applications, under the effect of the generalized displacement operator; The first one is the potential barriers and well, and the second one is an infinite potential well. In the first chapter, we discussed the usual reflection and transmission coefficients for potential barrier and well, as well as, the normalized wave functions and energies for infinite potential well. In the second chapter, the solutions of the Schrödinger equation for the harmonic oscillator and infinite potential well in the presence of the generalized displacement coefficient have been discussed. This is done by referring to two previous papers that dealt with the two systems. In the third chapter, we found new results, by applying the generalized displacement operator with the following generalized form of momentum operator P ̂_α=-iℏ(1+αx^2)d/dx, for potential barrier and well, and infinite potential well, where the main result is that the generalized displacement changes the length of the potential barrier and well, and infinite potential well: For the first application, we found that the transmission coefficient is increasing under the impact of generalized displacement operator, and vice versa for reflection coefficient. For the second application (infinite potential well), we concluded that the eigenvalues of energy and uncertainty of position decrease within the generalized displacement context, compared to the usual system. All these results are shown clearly by plots.