Abstract
The full set of resonant states in double and triple quantum well/barrier structures is investigated. This includes bound, anti-bound and normal resonant states which are all eigensolutions of Schrödinger’s equation with generalized outgoing wave boundary conditions. The transformation of resonant states and their transitions between different subgroups as well as the role of each subgroup in observables, such as the quantum transmission, is analyzed. The quantum well potentials are modeled by Dirac delta functions; therefore, as part of this study, the well known problem of bound states in delta-like potentials is also revisited.
Highlights
Resonant states (RSs) have been known in quantum mechanics for almost a century, since the pioneering works of Gamow [1] and Siegert [2]
The aim of this paper is to study the RSs of simple one-dimensional (1D) quantum-mechanical systems, such as double and triple quantum wells, for better understanding of their properties, as well as for generating an analytic basis of RSs for its further use in the resonant-state expansion (RSE) treating more complicated potentials
We have studied the full set of resonant states of a onedimensional Schrodinger problem with double and triple quantum wells or barriers approximated by Dirac delta functions
Summary
Resonant states (RSs) have been known in quantum mechanics for almost a century, since the pioneering works of Gamow [1] and Siegert [2]. The aim of this paper is to study the RSs of simple one-dimensional (1D) quantum-mechanical systems, such as double and triple quantum wells, for better understanding of their properties, as well as for generating an analytic basis of RSs for its further use in the RSE treating more complicated potentials. The spectral properties of quantum systems are not limited to bound states Rather, phenomena, such as quantum tunneling through barriers and quantum transmission and scattering of particles across the potential, are mainly determined by the internal resonances of the system, which are described by the RSs. These, to the best of our knowledge, have not been investigated so far even in such simple systems as 1D double and triple Dirac quantum wells or barriers. We investigate the role of the RSs in the quantum transmission
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