Wave packet scattering from time-varying potential barriers in one dimension

2014 ◽  
Vol 82 (2) ◽  
pp. 142-152 ◽  
Author(s):  
Robert M. Dimeo
Keyword(s):  
Wave Packet ◽  
One Dimension ◽  
Time Varying ◽  
Potential Barriers

scholarly journals Penetration into potential barriers in several dimensions

1937 ◽  
Vol 163 (915) ◽  
pp. 606-610 ◽  
Keyword(s):  
Refractive Index ◽  
Jacobi Equation ◽  
One Dimension ◽  
Practical Application ◽  
One Dimensional ◽  
Potential Barriers ◽  
Separable Problems ◽  
Total Reflexion ◽  
Similar Approximation ◽  
Hamilton Jacobi Equation

It is well known that in regions in which the refractive index varies sufficiently slowly, Schrödinger’s equation can be very simply treated by using its connexion with Hamilton-Jacobi’s differential equation. It is also known that a similar approximation is possible in regions of slowly varying imaginary refractive index (total reflexion). For the latter case the method was developed in papers by Jeffreys (1924), Wentzel (1926), Brillouin (1926) and Kramers (1926). These papers discuss also the behaviour of the wave function in the neighbourhood of the limit between the regions of real and imaginary refractive index. But although the connexion with the Hamilton-Jacobi equation holds in any number of dimensions, this equation can be solved by elementary means only in one dimension (or for problems that can by separation be reduced to one dimension), and for this reason the practical application of the method has so far been limited to one-dimensional or separable problems. In the present paper we discuss the case of more than one dimension and show that certain very simple inequalities may be obtained.

Generation of ultrafast spatiotemporal wave packet embedded with time-varying orbital angular momentum

2020 ◽  
Vol 65 (16) ◽  
pp. 1334-1336 ◽  
Author(s):  
Chenhao Wan ◽  
Jian Chen ◽  
Andy Chong ◽  
Qiwen Zhan
Keyword(s):  
Angular Momentum ◽  
Wave Packet ◽  
Orbital Angular Momentum ◽  
Time Varying

Resonant Tunneling of Fast Solitons through Large Potential Barriers

2011 ◽  
Vol 63 (6) ◽  
pp. 1201-1219 ◽  
Author(s):  
Walid K. Abou Salem ◽  
Catherine Sulem
Keyword(s):  
Schrödinger Equation ◽  
Nonlinear Schrödinger Equation ◽  
Resonant Tunneling ◽  
Schrodinger Equation ◽  
Nonlinear Schrodinger Equation ◽  
One Dimension ◽  
Potential Barriers ◽  
Nonlinear Schrödinger ◽  
Large Potential

AbstractWe rigorously study the resonant tunneling of fast solitons through large potential barriers for the nonlinear Schrödinger equation in one dimension. Our approach covers the case of general nonlinearities, both local and Hartree (nonlocal).

Colloidal Quantum Dots of III-V Semiconductors

MRS Bulletin ◽  
1998 ◽  
Vol 23 (2) ◽  
pp. 24-30 ◽  
Author(s):  
Arthur J. Nozik ◽  
Olga I. Mićić
Keyword(s):  
Quantum Wells ◽  
Epitaxial Film ◽  
Energy Levels ◽  
Epitaxial Films ◽  
Charge Carriers ◽  
One Dimension ◽  
Potential Barriers ◽  
Semiconductor Structures ◽  
Barrier Region ◽  
De Broglie Wavelength

Quantization effects in semiconductor structures were first demonstrated in the early 1970s in III-V quantum wells; these structures consisted of a thin epitaxial film of a smaller bandgap (Eg) semiconductor (e.g., GaAs, Eg = 1.42 eV) sandwiched between two epitaxial films of a larger bandgap semiconductor (e.g., Al0.3Ga0.7As, Eg = 2.0 eV). The conduction- and valence-band offsets of the two semiconductor materials produce potential barriers for electrons and holes, respectively. The smaller bandgap semiconductor constitutes the quantum-well region and the larger bandgap material the potential barrier region. If the film of the smaller bandgap material is sufficiently thin (thickness less than the de-Broglie wavelength of the charge carriers, which typically requires thicknesses less than about 300 Å for III-V semiconductors), then the charge carriers are confined in one dimension by the potential barriers, and quantization of the energy levels for both electrons and holes can occur (Figure 1).

scholarly journals KLEIN TUNNELING IN THE PRESENCE OF RANDOM IMPURITIES

2012 ◽  
Vol 23 (12) ◽  
pp. 1250080 ◽  
Author(s):  
S. PALPACELLI ◽  
M. MENDOZA ◽  
H. J. HERRMANN ◽  
S. SUCCI
Keyword(s):  
Fluid Dynamics ◽  
Wave Packet ◽  
Lattice Boltzmann ◽  
Random Media ◽  
Relativistic Quantum ◽  
Disordered Media ◽  
Potential Barriers ◽  
Klein Tunneling ◽  
Disordered Medium ◽  
Conductivity Loss

In this paper, we study Klein tunneling in random media. To this purpose, we simulate the propagation of a relativistic Gaussian wave packet through a disordered medium with randomly distributed potential barriers (impurities). The simulations, based on a relativistic quantum lattice Boltzmann (QLB) method, permit to compute the transmission coefficient across the sample, thereby providing an estimate for the conductivity (or permeability) as a function of impurity concentration and strength of the potentials. It is found that the conductivity loss due to impurities is significantly higher for wave packets of massive particles, as compared to massless ones. A general expression for the loss of conductivity as a function of the impurity percentage is presented and successfully compared with the Kozeny–Carman law for disordered media in classical fluid-dynamics.

Tunnelling time of a gaussian wave packet through two potential barriers

Open Physics ◽  
2005 ◽  
Vol 3 (3) ◽  
Author(s):  
Vittoria Petrillo ◽  
Vladislav Olkhovsky
Keyword(s):  
Wave Packet ◽  
Gaussian Wave Packet ◽  
Double Barrier ◽  
Potential Barriers ◽  
Hartman Effect ◽  
Spectrum Width ◽  
Quantum Wave ◽  
Tunnelling Time

AbstractThe resonant and non-resonant dynamies of a Gaussian quantum wave packet travelling through a double barrier system is studied as a function of the initial characteristics of the spectrum and of the parameters of the potential. The behaviour of the tunnelling time shows that there are situations where the Hartman effect occurs, while, when the resonances are dominant, and in particular for b>π/Δk (b being the inter-barrier distance and Δk the spectrum width), the tunnelling time becomes very large and the Hartman effect does not take place.

Distributed approximating function approach to time‐dependent wave‐packet propagation in more than one dimension: Inelastic collinear atom–diatom collisions

1993 ◽  
Vol 99 (2) ◽  
pp. 1028-1034 ◽  
Author(s):  
Youhong Huang ◽  
Donald J. Kouri ◽  
Mark Arnold ◽  
Thomas L. Marchioro ◽  
David K. Hoffman
Keyword(s):  
Wave Packet ◽  
Time Dependent ◽  
Function Approach ◽  
One Dimension
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