<i>Fundamentals of Quantum Mechanics: Particles, Waves and Wave Mechanics</i>

Borowitz, Sidney; Sposito, Garrison

doi:10.1063/1.3034787

Cited by 3 publications

(4 citation statements)

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“…where 𝑘 is the radial wavenumber and 𝑆(𝑟) is the eikonal [9,10]. In the lowest order by 1/𝑘 one can find the standard eikonal equation…”

Section: Solution Of Eikonal Equation For Unstable Perturbationsmentioning

confidence: 99%

Approximation of radial structure of unstable ion-sound modes in rotating magnetized plasma column by eikonal equation

Marusov

2022

Discrete and Continuous Models

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The problem of the correct asymptotic construction of the radial structure of linearly unstable ion-sound electrostatic eigenmodes is studied. The eigenvalue problem with boundary conditions of the first and second kind (electrodynamic and hydrodynamic types) for the oscillations that propagate in a uniform cylindrical column of magnetized plasma along an axial homogeneous magnetic field is formulated. A method for constructing a discrete spectrum of small-scale unstable oscillations of the system based on the basic principles of geometric optics is proposed. The main idea of the method is an explicit idea of the type of boundary conditions - the conductivity and absorbing properties of the wall bounding the plasma cylinder. A dispersion relation for unstable small-scale modes destabilized due to the effects of differential rotation is derived from the Eikonal equation. For the correct construction instability growth rates spectra an universal recipe for the selection of radial wave numbers of small-scale eigenmodes in accordance with any of the types of boundary conditions is proposed.

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“…where 𝑘 is the radial wavenumber and 𝑆(𝑟) is the eikonal [9,10]. In the lowest order by 1/𝑘 one can find the standard eikonal equation…”

Section: Solution Of Eikonal Equation For Unstable Perturbationsmentioning

confidence: 99%

Approximation of radial structure of unstable ion-sound modes in rotating magnetized plasma column by eikonal equation

Marusov

2022

Discrete and Continuous Models

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“…The tunneling probability for carriers encountering a potential barrier is determined by using the Wentzel-KramerBrillouin approximation. By assuming a triangular potential barrier, the tunneling probability at an electric field F is [22] |T | 2 = exp −2…”

Section: Numerical Simulationmentioning

confidence: 99%

Monte Carlo Simulation of Hot Carrier Transport in Heterogeneous Ge/${\rm Al}_{x}{\rm Ga}_{1-x}{\rm As}~(0\leq x\leq 0.8)$ Multilayer Avalanche Photodiodes

Chia

Dalapati

2013

IEEE Trans. Electron Devices

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Impact ionization in novel Ge/Al x Ga 1−x As (0≤ x ≤ 0.8) multilayer structures is investigated using numerical simulation. The simulated effective electron (ᾱ) and hole (β) ionization coefficients reveal that a largeβ/ᾱ ratio of up to 8 can be obtained in a 25-period Ge (50 nm)/Al 0.8 Ga 0.2 As (50 nm) multilayer structure, much larger than that in the Ge and Al x Ga 1−x As homojunctions, attributed by the reduction inᾱ. The substantial difference in phonon scattering cross-sections in the Al x Ga 1−x As barrier and the Ge well played an important role in determining theβ/ᾱ ratio in these structures. Breakdown voltage analysis indicates that hot carriers' drift in the Al x Ga 1−x As barriers and Ge wells sampled the transport properties of both materials, despite the electron and hole ionizations are dominated by that of Ge within the electric field range studied.

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“…Em vários livros-texto [1], a conexão entre a mecânica quântica e a clássicaé realizada ao se fazer uso do teorema de Ehrenfest [2] e/ou da approximação WKB [3][4][5]. O primeiro consiste em deduzir as equações…”

Section: Introductionunclassified

“…As equações (1) e (2) são válidas desde que o potencial externo V varie vagarosamente dentro de um pacote de onda bem localizado ψ P E (Pacote de Ehrenfest). Assim, de acordo com os livros-texto [1], as equações de Newton são obtidas como limite clássico da equação de Schrödinger. No entanto, Ballentine et al [6,7] (veja também [8,9] + V (q, t) = 0…”

Section: Introductionunclassified

Limite clássico da mecânica quântica

Bolivar

2003

Rev. Bras. Ensino Fís.

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Neste trabalho, apresentamos um procedimento alternativo para o cálculo do limite clássico ( → 0) das equações de movimento da mecânica quântica. Comparamos nosso método com o teorema de Ehrenfest, a aproximação WKB e com o potencial quântico de Bohm Q → 0. Segue, também, a tradução de um artigo do Einstein sobre a problemática da conexão entre as teorias clássica e quântica.In this work we propose an alternative procedure to calculate the classical limit ( → 0) of the quantum mechanical equations of motion. We compare our method with the Ehrenfest theorem, the WKB approximation and the Bohm quantum potential Q → 0. We also translate an Einstein's paper about the relation between quantum and classical theories. I IntroduçãoEm vários livros-texto [1], a conexão entre a mecânica quântica e a clássicaé realizada ao se fazer uso do teorema de Ehrenfest [2] e/ou da approximação WKB [3][4][5]. O primeiro consiste em deduzir as equaçõesa partir da equação de Schrödinger + Q(q, t) + V (q, t) = 0,

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Fundamentals of Quantum Mechanics: Particles, Waves and Wave Mechanics

Cited by 3 publications

References 0 publications

Approximation of radial structure of unstable ion-sound modes in rotating magnetized plasma column by eikonal equation

Approximation of radial structure of unstable ion-sound modes in rotating magnetized plasma column by eikonal equation

Monte Carlo Simulation of Hot Carrier Transport in Heterogeneous Ge/${\rm Al}_{x}{\rm Ga}_{1-x}{\rm As}~(0\leq x\leq 0.8)$ Multilayer Avalanche Photodiodes

Limite clássico da mecânica quântica

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