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Plots of the absolute values of the anti-bound state, 1 st , 2 nd, and 3 rd resonant states wave functions.
Source publication
In this work, the concept of resonant states (RSs) in a finite square quantum well is presented. We first derive the analytic secular transcendental equations for even and odd states by applying the outgoing wave boundary conditions into the one-dimensional Schrödinger’s wave equation. The complex solution of these equations is found using the nume...
Contexts in source publication
Context 1
... bound states, they have a solution for the continuous range of energies which satisfies E <0. It diverges exponentially for large | í µí±¥ |(see fig.2). The solution inside the well is similar to that of the bound state. ...
Context 2
... can see the wave function is symmetric around the origin, which indicates that there must be solutions of defined parity also for anti-bound states. Figure 2 shows the plots of the absolute values of the anti-bound state, 1 st , 2 nd, and 3 rd normal RSs wave functions while figure 3 shows the 5 th and 10 th normal RSs wave functions. They show a similar behavior to the bound states wave functions having a defined parity within the well. ...
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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 Schr...
Citations
... RSs have been studied for quite a long time (Siegert, 1939;Gamow, 1928). In quantum mechanics, they are referred to as the stationary states solution to the Schrödinger equation with purely boundary conditions of only outgoing waves (Hatano, 2008;Tanimu and Bagudo, 2020). These boundary conditions strictly define RSs. ...
Study’s Excerpt The rigorous resonant-state expansion (RSE) method is extended to the non-relativistic one-dimensional wave equation. Resonant states (RSs) wave numbers as the unperturbed basis were employed to confirm the RSE's convergence to exact solutions. RSE's has potentials for systematically calculating RSs in complex quantum systems with multi-well potentials. Full Abstract The resonant-state expansion (RSE), a rigorous perturbation theory recently developed in electrodynamics, is here applied to the non-relativistic wave equation in one-dimension. The resonant states (RSs) wave numbers for the double well system are analytically calculated and used as the unperturbed basis for calculating the RSE. We demonstrate the efficiency of the RSE by verifying its convergence to the exact solution for a triple well potential. We show that for the chosen perturbations (i.e., for and ), the method is particularly suitable for calculating all the RSs within the spectrum.
