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21. DETERMINATION OF RESONANT STATES IN A FINITE SQUARE WELL by S. Kado and A. Tanimu Volume 54 (January 2020 Issue)
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DETERMINATION OF RESONANT STATES IN A FINITE SQUARE WELL

S. Kado and A. Tanimu


Department of Physics, Federal University Dutsinma, Katsina.

Department of Physics, Umaru Musa Yar’adua University, Katsina.


Abstract

The purpose of this work is to determine the resonant states in a one-dimensional finite square well system. Resonant states are the Eigen solutions to the time independent Schrödinger’s equation with outgoing wave boundary conditions. The secular transcendental equations for even and odd states were first obtained. This is done by solving the Schrödinger’s wave equation with purely outgoing wave boundary conditions. The equations obtained were solved numerically in MATLAB leading to three types of states namely: bound states, antibound states and resonant states. Apart from bound states which has been covered in so many textbooks resonant states have attracted significant interest in recent time, in particular, in quantum mechanics due to rapid progress in the field of semiconductor physics were different electronic states are formed. In spite of this growing interest, many fundamental aspects of resonant states are still to be investigated. In this case the effect of changing the parameters in the system is fully observed. We observed that for a shallow well there is at least one bound state within the system. However, increasing the strength of the potential will lead to an increase in the number of bound/antibound states.


Keywords: Finite Square well, Bound states, Antibound states, Resonant states.

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