scholarly journals Tutorial: The quantum finite square well and the Lambert W function

2017 ◽  
Vol 95 (2) ◽  
pp. 105-110 ◽  
Author(s):  
Ken Roberts ◽  
S.R. Valluri
Keyword(s):  
Quantum Mechanics ◽  
Energy Levels ◽  
Inverse Image ◽  
Lambert W Function ◽  
Infrared Photodetector ◽  
Additional Insight ◽  
One Dimensional ◽  
Quantum Well Infrared Photodetector ◽  
Square Well ◽  
Insight Into

We present a solution of the quantum mechanics problem of the allowable energy levels of a bound particle in a one-dimensional finite square well. The method is a geometric-analytic technique utilizing the conformal mapping w → z = wew between two complex domains. The solution of the finite square well problem can be seen to be described by the images of simple geometric shapes, lines, and circles, under this map and its inverse image. The technique can also be described using the Lambert W function. One can work in either of the complex domains, thereby obtaining additional insight into the finite square well problem and its bound energy states. This suggests interesting possibilities for the design of materials that are sensitive to minute changes in their environment such as nanostructures and the quantum well infrared photodetector.

scholarly journals A resurgence analysis for cubic and quartic anharmonic potentials

2017 ◽  
Vol 32 (05) ◽  
pp. 1750033 ◽  
Author(s):  
Ilmar Gahramanov ◽  
Kemal Tezgin
Keyword(s):  
Quantum Mechanics ◽  
Energy Levels ◽  
Resonance Energy ◽  
One Dimensional

In this work, we explicitly show resurgence relations between perturbative and one instanton sectors of the resonance energy levels for cubic and quartic anharmonic potentials in one-dimensional quantum mechanics. Both systems satisfy the Dunne–Ünsal relation and hence we are able to derive one-instanton nonperturbative contributions with the fluctuation terms to the energy merely from the perturbative data. We confirm our results with previous results obtained in the literature.

Quasi-one-dimensional gold grating with Si3N4cap layer as optical coupler for AlGaN/GaN quantum well infrared photodetector

2015 ◽  
Vol 13 (5-6) ◽  
pp. 304-306
Author(s):  
Shuai Wang ◽  
Feng Wu ◽  
Jun Zhang ◽  
Hanling Long ◽  
Zheng Gong ◽  
...  
Keyword(s):  
Quantum Well ◽  
Infrared Photodetector ◽  
Optical Coupler ◽  
One Dimensional ◽  
Quantum Well Infrared Photodetector

Transient Wave Propagation in a Harmonically Heterogeneous Elastic Solid

1992 ◽  
Vol 59 (2S) ◽  
pp. S145-S151
Author(s):  
Hyun-Sil Kim ◽  
Jerry H. Ginsberg
Keyword(s):  
Floquet Theory ◽  
Elastic Solid ◽  
Harmonic Excitation ◽  
Additional Insight ◽  
Regular Perturbation ◽  
Transient Wave ◽  
One Dimensional ◽  
Dilatational Wave ◽  
Transient Wave Propagation ◽  
Insight Into

Transient propagation of a one-dimensional dilatational wave in a harmonically heterogeneous elastic solid is studied by several techniques. A regular perturbation analysis in terms of the characteristics of the differential equation shows that initiation of a temporally harmonic excitation that generates a signal whose wavelength is twice the periodicity of the heterogeneity leads to secularity in the first approximation. The frequency at which this situation occurs matches the frequency at which Floquet theory predicts that steady-state waves may be unstable. A finite difference algorithm based on integrating along the characteristics is developed and implemented to obtain a numerical solution. In the critical case, backscattering of the wave from the heterogeneity results in a mixture of propagating and standing wave features. However, rather than being unstable, the heterogeneity in this condition is shown to result in maximum interference with forward propagation. A comparable analysis for a step excitation on the boundary provides additional insight into the underlying propagation phenomena.

scholarly journals Leaky Modes of Waveguides as a Classical Optics Analogy of Quantum Resonances

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Sara Cruz y Cruz ◽  
Oscar Rosas-Ortiz
Keyword(s):  
Quantum Mechanics ◽  
Short Range ◽  
Bound States ◽  
Waveguide Structure ◽  
One Dimensional ◽  
Leaky Modes ◽  
Scattering States ◽  
Quantum Resonances ◽  
Zone Of Influence ◽  
Square Well

A classical optics waveguide structure is proposed to simulate resonances of short range one-dimensional potentials in quantum mechanics. The analogy is based on the well-known resemblance between the guided and radiation modes of a waveguide with the bound and scattering states of a quantum well. As resonances are scattering states that spend some time in the zone of influence of the scatterer, we associate them with the leaky modes of a waveguide, the latter characterized by suffering attenuation in the direction of propagation but increasing exponentially in the transverse directions. The resemblance is complete because resonances (leaky modes) can be interpreted as bound states (guided modes) with definite lifetime (longitudinal shift). As an immediate application we calculate the leaky modes (resonances) associated with a dielectric homogeneous slab (square well potential) and show that these modes are attenuated as they propagate.

Sound Synthesis of a Gaussian Quantum Particle in an Infinite Square Well

2014 ◽  
Vol 38 (4) ◽  
pp. 53-67 ◽  
Author(s):  
Rodrigo F. Cádiz ◽  
Javier Ramos
Keyword(s):  
Wave Packet ◽  
Dynamic Behavior ◽  
Quantum Particle ◽  
Point Of View ◽  
One Dimensional ◽  
Quantum Revivals ◽  
Proposed Model ◽  
State Evolution ◽  
Square Well ◽  
Insight Into

This article describes a synthesis technique based on the sonification of the dynamic behavior of a quantum particle enclosed in an infinite square well. More specifically, we sonify the momentum distribution of a one-dimensional Gaussian bouncing wave packet model. We have chosen this particular case because of its relative simplicity and interesting dynamic behavior, which makes it suitable for a novel sonification mapping that can be applied to standard synthesis techniques, resulting in the generation of appealing sounds. In addition, this sonification might provide useful insight into the behavior of the quantum particle. In particular, this model exhibits quantum revivals, minimizes uncertainty, and exhibits similarities to the case of a classical bouncing ball. The proposed model has been implemented in real time in both the Max/MSP and the Pure Data environments. The algorithm is based on concepts of additive synthesis where each oscillator describes the eigenfunctions that characterize the state evolution of the wave packet. We also provide an analysis of the sounds produced by the model from both a physical and a perceptual point of view.

Structure and function of neural networks in the retina

1988 ◽  
Vol 46 ◽  
pp. 26-27
Author(s):  
Peter Sterling
Keyword(s):  
Ganglion Cells ◽  
Three Dimensional ◽  
Structure And Function ◽  
Synaptic Connections ◽  
Visual Axis ◽  
One Dimensional ◽  
Cat Retina ◽  
Ultrathin Sections ◽  
And Function ◽  
Insight Into

The synaptic connections in cat retina that link photoreceptors to ganglion cells have been analyzed quantitatively. Our approach has been to prepare serial, ultrathin sections and photograph en montage at low magnification (˜2000X) in the electron microscope. Six series, 100-300 sections long, have been prepared over the last decade. They derive from different cats but always from the same region of retina, about one degree from the center of the visual axis. The material has been analyzed by reconstructing adjacent neurons in each array and then identifying systematically the synaptic connections between arrays. Most reconstructions were done manually by tracing the outlines of processes in successive sections onto acetate sheets aligned on a cartoonist's jig. The tracings were then digitized, stacked by computer, and printed with the hidden lines removed. The results have provided rather than the usual one-dimensional account of pathways, a three-dimensional account of circuits. From this has emerged insight into the functional architecture.

Classification of Infant Vocalizations by Untrained Listeners

2019 ◽  
Vol 62 (9) ◽  
pp. 3265-3275
Author(s):  
Heather L. Ramsdell-Hudock ◽  
Anne S. Warlaumont ◽  
Lindsey E. Foss ◽  
Candice Perry
Keyword(s):  
Formal Education ◽  
Additional Insight ◽  
Listener Responses ◽  
Infant Vocalization ◽  
Early Infant ◽  
Infant Vocalizations ◽  
Audio Recordings ◽  
Speech And Language Development ◽  
Insight Into

Purpose To better enable communication among researchers, clinicians, and caregivers, we aimed to assess how untrained listeners classify early infant vocalization types in comparison to terms currently used by researchers and clinicians. Method Listeners were caregivers with no prior formal education in speech and language development. A 1st group of listeners reported on clinician/researcher-classified vowel, squeal, growl, raspberry, whisper, laugh, and cry vocalizations obtained from archived video/audio recordings of 10 infants from 4 through 12 months of age. A list of commonly used terms was generated based on listener responses and the standard research terminology. A 2nd group of listeners was presented with the same vocalizations and asked to select terms from the list that they thought best described the sounds. Results Classifications of the vocalizations by listeners largely overlapped with published categorical descriptors and yielded additional insight into alternate terms commonly used. The biggest discrepancies were found for the vowel category. Conclusion Prior research has shown that caregivers are accurate in identifying canonical babbling, a major prelinguistic vocalization milestone occurring at about 6–7 months of age. This indicates that caregivers are also well attuned to even earlier emerging vocalization types. This supports the value of continuing basic and clinical research on the vocal types infants produce in the 1st months of life and on their potential diagnostic utility, and may also help improve communication between speech-language pathologists and families.

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