Phase-Amplitude Relations for a Particle with a Superposition of Two Energy Levels in a Double Potential Well

We study the connection between the phase and the amplitude of the wave function and the conditions under which this relationship exists. For this we use model of particle in a box. We have shown that the amplitude can be calculated from the phase and vice versa if the log Analytical uncertainty relations are satisfied.

Возбуждение и ионизация частицы в одномерной потенциальной яме нулевого радиуса предельно коротким световым импульсом

The Migdal sudden perturbation approximation is used to solve the problem of excitation and ionization particles in a one-dimensional potential of zero radius with an extremely short pulse. There is has only one energy level in such a one-dimensional the delta-shaped potential well. It is shown that for pulse durations shorter than the characteristic period of oscillations of the wave function of the particle in the bound state, the population of the level (and the probability of ionization) is determined by the ratio of the electric the area of ​​the pulse to the characteristic “scale” of the area inversely proportional to the area of ​​localization of the particle in a bound state.

Performance enhancement of armchair graphene nanoribbon resonant tunneling diode using V-shaped potential well

We study the electron transport in armchair graphene nanoribbon (AGNR) resonant tunneling diode (RTD) using square and V-shaped potential well profiles. We use non-equilibrium Green’s function formalism to analyze the transmission and I-V characteristics. Results show that an enhancement in the peak current (Ip ) can be obtained by reducing the well width (Ww ) or barrier width (Wb ). As Ww decreases, Ip shifts to a higher peak voltage (Vp ), while there is almost no change in Vp with decreasing Wb . It is gratifying to note that there is an enhancement in Ip by about 1.6 times for a V-shaped well over a square well. Furthermore, in the case of a V-shaped well, the negative differential resistance occurs in a shorter voltage range, which may beneficial for ultra-fast switching and high-frequency signal generation. Our work anticipates the suitability of graphene, having better design flexibility, to develop ideally 2D RTDs for use in ultra-dense nano-electronic circuits and systems.

Existence result for critical Klein-Gordon-Maxwell system involving steep potential well

This paper deals with the following system \begin{equation*} \left\{\begin{aligned} &{-\Delta u+ (\lambda A(x)+1)u-(2\omega+\phi) \phi u=\mu f(u)+u^{5}}, & & {\quad x \in \mathbb{R}^{3}}, \\ &{\Delta \phi=(\omega+\phi) u^{2}}, & & {\quad x \in \mathbb{R}^{3}}, \end{aligned}\right. \end{equation*} where $\lambda, \mu>0$ are positive parameters. Under some suitable conditions on $A$ and $f$, we show the boundedness of Cerami sequence for the above system by adopting Poho\v{z}aev identity and then prove the existence of ground state solution for the above system on Nehari manifold by using Br\’{e}zis-Nirenberg technique, which improve the existing result in the literature.

Black Holes as Geometric Distortional Extrema

It is shown in the present work that the distorted-space model of matter as extended to extreme curvature limits results in characteristics mimicking those of galactic-holes. The distorted-geometry structures exhibit non-Newtonian features wherein the hole or core-region fields of the structures are energetically-repulsive (negative pressure), do not behave functionally in an r-4 manner and terminate at zero at the radial origin (no singularity). Of particular interest is that of r-6 energy-density behavior at structural radial distances near the core of the distortion, a region also displaying potential-well behavior.

Time Delay in Electron Collision with a Spherical Target as a Function of the Scattering Angle

We have studied the angular time delay in slow-electron elastic scattering by spherical targets as well as the average time delay of electrons in this process. It is demonstrated how the angular time delay is connected to the Eisenbud–Wigner–Smith (EWS) time delay. The specific features of both angular and energy dependencies of these time delays are discussed in detail. The potentialities of the derived general formulas are illustrated by the numerical calculations of the time delays of slow electrons in the potential fields of both absolutely hard-sphere and delta-shell potential well of the same radius. The conducted studies shed more light on the specific features of these time delays.

Distortional Extrema and Holes in the Geometric Manifold

It is shown in the present work that the distorted-space model of matter as extended to extreme curvature limits results in characteristics mimicking those of galactic-holes. The distorted-geometry structures exhibit non-Newtonian features wherein the hole or core-region fields of the structures are energetically-repulsive (negative pressure), do not behave functionally in an r-4 manner and terminate at zero at the radial origin (no singularity). Of particular interest is that of r-6 energy-density behavior at structural radial distances near the core of the distortion, a region also displaying potential-well behavior.