Resonances of a Potential Well with a Thick Barrier (original) (raw)
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Above-barrier resonances: analytical expressions for energy and width
Journal of Physics A: Mathematical and General, 2002
We construct a smooth realistic barrier potential that can generate resonances above the top of the barrier provided a parameter λ controlling the flatness of the barrier is larger than the critical value λ = √ 2. The energies and widths of resonances are expressed analytically in terms of the characteristics of the barrier, namely height, range and flatness. In order to obtain a more versatile and asymmetric barrier, two symmetric barriers are merged together side by side and the exact transmission coefficient across such a barrier is derived.
Open Mathematics
In Applied Mathematics Letters 74 (2017), 147–153, the Hyers-Ulam stability of the one-dimensional time-independent Schrödinger equation was investigated when the relevant system has a potential well of finite depth. As a continuous work, we prove in this paper a type of Hyers-Ulam stability of the one-dimensional time-independent Schrödinger equation with a rectangular potential barrier of {V}_{0} in height and 2c in width, where {V}_{0} is assumed to be greater than the energy E of the particle under consideration.
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We give the quantization condition and the semiclassical distribution of resonances of the Schrödinger operator in a general setting where the trapped set of the underlying classical mechanics makes a finite graph consisting of hyperbolic fixed points and associated homoclinic and heteroclinic trajectories. This is one of the results in our paper [3]. We give some examples and a rough sketch of the proof.
ABOUT QUANTUM WELLS AND QUANTUM BARRIERS
A particular discussion of the ground state energy level and the corresponding wave function shape is discussed for quantum well systems aiming to provide a better comprehension of such confinement effects for quantum mechanics beginners. The results have been numerically obtained from the solution of one dimensional time independent Schrödinger equation for a confined space inside which either a barrier or a quantum well is grown. The wave function and energy level for the ground state is extensively analyzed in both scenarios, when the inserted barrier height increases considerably and when the inserted quantum well becomes extremely thin and deeper simulating a delta-doped system. The physics interpretations of these results are particularly rich and may become useful to undergraduate students not only of physics courses but also for other domains where structural concepts of quantum theory are necessary, required or wanted.
A Discrete Model for Resonance Near Embedded Bound States
IEEE Photonics Journal, 2010
We present a discrete model for resonance in periodic dielectric slabs arising from the interaction of electromagnetic plane waves with guided modes at frequencies embedded in the continuum. Two infinite rows of interacting masses in the model support propagating and evanescent waves simultaneously. This allows for modes exponentially trapped near an obstacle at continuum frequencies. The discrete model manifests resonant transmission features of the periodic slab and it includes parameters of asymmetry that are connected to the detuning of the resonance. Moreover, resonant transmission in both systems is described by a rigorous universal formula that explicitly incorporates a detuning parameter.