Transmission and reflection of a wave packet with a small width in one-dimensional quantum mechanics

2003 ◽  
Vol 81 (10) ◽  
pp. 1205-1214 ◽  
Author(s):  
F M Toyama ◽  
Y Nogami
Keyword(s):  
Quantum Mechanics ◽  
Wave Packet ◽  
Plane Wave ◽  
Incident Wave ◽  
Wave Incident ◽  
One Dimensional ◽  
Small Width ◽  
Bohm Trajectories ◽  
Potential Area ◽  
Transmission And Reflection

The transmission and the reflection of a wave incident on a potential in one-dimensional quantum mechanics are usually discussed by assuming that a plane wave eikx or a broad wave packet is incident. We are interested in what happens if the width of the incident wave packet is very small. In this case, the incident wave packet can spread out in such a way that part of the wave packet turns around before reaching the potential area and proceeds backward. This can clearly be visualized by means of the Bohm trajectories associated with the wave packet. We discuss a complication that arises in this case regarding the notion of the reflection probability.PACS Nos.: 03.65–w, 03.65.Nk

REFLECTION FROM A WIRE GRID PARALLEL TO A CONDUCTING PLANE

1954 ◽  
Vol 32 (9) ◽  
pp. 571-579 ◽  
Author(s):  
James R. Wait
Keyword(s):  
Plane Wave ◽  
Transmission Line ◽  
Incident Wave ◽  
Electric Vector ◽  
Wave Incident ◽  
Conducting Surface ◽  
Conducting Plane ◽  
Wire Grid ◽  
Parallel Wire ◽  
Plane Wave Incident

A solution is outlined for the problem of a plane wave incident obliquely on a parallel-wire grid which is backed by a plane conducting surface. The electric vector of the incident wave is taken to be parallel to the grid wires. The equivalent transmission line problem is pointed out. It is shown that, in certain cases, a resistive wire grid will absorb all the energy in the incident wave.

scholarly journals IMPLICATIONS OF A QUANTUM MECHANICAL TREATMENT OF THE UNIVERSE

1998 ◽  
Vol 13 (05) ◽  
pp. 347-351 ◽  
Author(s):  
MURAT ÖZER
Keyword(s):  
Quantum Mechanics ◽  
Wave Packet ◽  
Early Universe ◽  
Mechanical Treatment ◽  
Correspondence Principle ◽  
Scale Factor ◽  
Quantum Mechanical ◽  
Quantum Mechanical Treatment ◽  
The Standard Model ◽  
The Universe

We attempt to treat the very early Universe according to quantum mechanics. Identifying the scale factor of the Universe with the width of the wave packet associated with it, we show that there cannot be an initial singularity and that the Universe expands. Invoking the correspondence principle, we obtain the scale factor of the Universe and demonstrate that the causality problem of the standard model is solved.

scholarly journals AdS2 × S2 × CY2 solutions in Type IIB with 8 supersymmetries

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Yolanda Lozano ◽  
Carlos Nunez ◽  
Anayeli Ramirez
Keyword(s):  
Quantum Mechanics ◽  
Riemann Surface ◽  
Central Charge ◽  
Global Solutions ◽  
Infinite Family ◽  
Dimensional System ◽  
One Dimensional

Abstract We present a new infinite family of Type IIB supergravity solutions preserving eight supercharges. The structure of the space is AdS2 × S2 × CY2 × S1 fibered over an interval. These solutions can be related through double analytical continuations with those recently constructed in [1]. Both types of solutions are however dual to very different superconformal quantum mechanics. We show that our solutions fit locally in the class of AdS2 × S2 × CY2 solutions fibered over a 2d Riemann surface Σ constructed by Chiodaroli, Gutperle and Krym, in the absence of D3 and D7 brane sources. We compare our solutions to the global solutions constructed by Chiodaroli, D’Hoker and Gutperle for Σ an annulus. We also construct a cohomogeneity-two family of solutions using non-Abelian T-duality. Finally, we relate the holographic central charge of our one dimensional system to a combination of electric and magnetic fluxes. We propose an extremisation principle for the central charge from a functional constructed out of the RR fluxes.

scholarly journals Topological correlators and surface defects from equivariant cohomology

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Rodolfo Panerai ◽  
Antonio Pittelli ◽  
Konstantina Polydorou
Keyword(s):  
Quantum Mechanics ◽  
Equivariant Cohomology ◽  
Surface Defects ◽  
Star Product ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Dimensional System ◽  
The Novel ◽  
One Dimensional ◽  
Dual Quantum

Abstract We find a one-dimensional protected subsector of $$ \mathcal{N} $$ N = 4 matter theories on a general class of three-dimensional manifolds. By means of equivariant localization we identify a dual quantum mechanics computing BPS correlators of the original model in three dimensions. Specifically, applying the Atiyah-Bott-Berline-Vergne formula to the original action demonstrates that this localizes on a one-dimensional action with support on the fixed-point submanifold of suitable isometries. We first show that our approach reproduces previous results obtained on S3. Then, we apply it to the novel case of S2× S1 and show that the theory localizes on two noninteracting quantum mechanics with disjoint support. We prove that the BPS operators of such models are naturally associated with a noncom- mutative star product, while their correlation functions are essentially topological. Finally, we couple the three-dimensional theory to general $$ \mathcal{N} $$ N = (2, 2) surface defects and extend the localization computation to capture the full partition function and BPS correlators of the mixed-dimensional system.

scholarly journals Splitting of degenerate states in one-dimensional quantum mechanics

2012 ◽  
Vol 127 (3) ◽  
Author(s):  
Avik Dutt ◽  
Trisha Nath ◽  
Sayan Kar ◽  
Rajesh Parwani
Keyword(s):  
Quantum Mechanics ◽  
One Dimensional ◽  
Degenerate States

scholarly journals A Broadband Ultrathin Nonlinear Switching Metamaterial

2017 ◽  
Vol 6 (2) ◽  
pp. 64
Author(s):  
E. Zarnousheh Farahani ◽  
S. Jarchi ◽  
A. Keshtkar
Keyword(s):  
Incident Wave ◽  
Optimization Method ◽  
Resonant Mode ◽  
Unit Cell ◽  
Incident Power ◽  
Full Wave ◽  
Effective Impedance ◽  
Nonlinear Simulations ◽  
Switching Property ◽  
Transmission And Reflection

In this paper, an ultrathin planar nonlinear metamaterial slab is designed and simulated. Nonlinearity is provided through placing diodes in each metamaterial unit cell. The diodes are auto-biased and activated by an incident wave. The proposed structure represents a broadband switching property between two transmission and reflection states depending on the intensity of the incident wave. High permittivity values are presented creating a near zero effective impedance at low power states, around the second resonant mode of the structure unit cell; as the result, the incident wave is reflected. Increasing the incident power to the level which can activate the loaded diodes in the structure results in elimination of the resonance and consequently a drop in the permittivity values near the permeability one as well as a switch to the transmission state. A full wave as well as a nonlinear simulations are performed. An optimization method based on weed colonization is applied to the unit cell of the metamaterial slab to achieve the maximum switching bandwidth. The structure represents a 24% switching bandwidth of a 10 dB reduction in the reflection coefficient.

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