Related papers: Lambert W Lines and Finite Square Well Sensors
Analytical calculations based on a Landau Level (LL) picture are reported for an interface (with a finite-width Quantum Well (QW)) and for a fully three-dimensional charged quantum electronic system in an external magnetic field. They lead…
For a quantum mechanical system with broken supersymmetry, we present a simple method of determining the ground state when the corresponding energy eigenvalue is sufficiently small. A concise formula is derived for the approximate ground…
An infinite sequence of potential well functions is considered. A trial wavefunction is used with the Schr$\ddot{\text{o}}$dinger equation to obtain an approximate ground state energy for each potential well function. We obtain an…
Edge states reflect the key physical properties yet are difficult to probe individually, particularly when several states are present at an edge. We present momentum resolved tunneling spectroscopy between a quantum well and a quantum wire…
A chart for the quantum mechanics of a particle of mass $m$ in a one-dimensional potential well of width $w$ and depth $V_0$ is derived. The chart is obtained by normalizing energy and potential through multiplication by ${8 m}{w^2} / h^2$,…
We establish a quantitative rigidity estimate for two-well frame-indifferent nonlinear energies, in the case in which the two wells have exactly one rank-one connection. Building upon this novel rigidity result, we then analyze solid-solid…
The results obtained by analyzing signals with the Square Wave Method (SWM) introduced previously can be presented in the frequency domain clearly and precisely by using the Square Wave Transform (SWT) described here. As an example, the SWT…
Garrett's approximation for the calculation of bound states energy in square wells is applied in a consistent way. So, one obtains simple formulas for these energies, with errors of about 1% for moderate, and 0.01% for deep wells. The…
A method for a calculation of quantum capacitance for a two-dimesional electron gas (2DEG) in potential wells of complicated geometry on the base of a quantum wave impedance technique was proposed. The application of this method was…
We derive and analyse well-posed boundary conditions for the linear shallow water wave equation. The analysis is based on the energy method and it identifies the number, location and form of the boundary conditions so that the initial…
A simple formalism for exploring quantum scattering and possible bound states in an arbitrary symmetric and localized potential in a unified way is presented. The symmetric square barrier and well potentials are used for illustrating the…
We determine approximate eigenvalues and eigenfunctions shapes for bound states in the $3D$ shallow spherical ultrarelativistic well. Existence thresholds for the ground state and first excited states are identified, both in the purely…
We give a lower bound for the energy of a quantum particle in the infinite square well. We show that the bound is exact and identify the well-known element that fulfils the equality. Our approach is not directly dependent on the…
We establish a rigorous mathematical framework connecting graphene nanoribbon quantum sensing to the Lambert W function through the finite square well (FSW) analogy. The Lambert W function, defined as the inverse of $f(W) = We^W$, provides…
We develop the formalism of quantum mechanics on three dimensional fuzzy space and solve the Schr\"odinger equation for a free particle, finite and infinite fuzzy wells. We show that all results reduce to the appropriate commutative limits.…
We study an anti-symmetric (square) well and barrier potential of depth/height $(V_0)$ placed between two rigid walls. Unlike the usual double-well, here the closely lying sub-barrier doublets need not be the lowest ones in the spectrum.…
In the present paper we propose the van der Waals-like model, which allows a purely analytical study of fluid properties including the equation of state, phase behavior and supercritical fluctuations. We take a square-well system as an…
Momentum resolved magneto-tunnelling spectroscopy is performed at a single sharp quantum Hall edge. We directly probe the structure of individual integer quantum Hall (QH) edge modes, and find that an epitaxially overgrown cleaved edge…
We apply power series expansion to symmetric multi-well oscillators bounded by two infinite walls. The spectrum and expectation values obtained are compared with available exact and approximate values for the unbounded ones. It is shown…
Computer simulations with Synopsys' Sentaurus TCAD of opto-electrical characteristics of separate-confinement heterostructure laser based on AlGaAs are used as an example to study the role of the width and depth of Quantum Well (QW) active…