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A Poisson-Boltzmann approach is used to determine the double-layer integral and differential capacitances in a finite-length situation for an electrolytic cell. By means of simple analytical calculations, it is shown how these quantities…
There are several definitions of energy density in quantum mechanics. These yield expressions that differ locally, but all satisfy a continuity equation and integrate to the value of the expected energy of the system under consideration.…
Impressive progress in the control of atomically thin crystals is now enabling the realization of gated structures in which two electrodes are separated by atomic scale distances. The electrical capacitance of these structures is determined…
A simple approximate solution for the quantum-mechanical quartic oscillator $V= m^2 x^2+g x^4$ in the double-well regime $m^2<0$ at arbitrary $g \geq 0$ is presented. It is based on a combining of perturbation theory near true minima of the…
In this article we present a study of the effects of hydrostatic pressure on the energy levels of a quantum dot with an electron. A quantum dot is modeled using an infinite potential well and a two-dimensional harmonic oscillator and solved…
We show that it needs a more delicate potential to confine particles inside a well. The original model containing a vague notation of infinity in the potential energy is ambiguous. Using the Heaviside step function and the Dirac…
Electrostatic confinement in semiconductors provides a flexible platform for the emulation of interacting electrons in a two-dimensional lattice, including in the presence of gauge fields. This combination offers the potential to realize a…
The quantum mechanical tunneling through multiple quantum barriers is a long-standing and well-known problem. Three methods proposed earlier to calculate the tunneling probabilities and energy splitting: (1). Instanton Method (2) WKb…
The two-dimensional topological insulator phase has been observed previously in single HgTe-based quantum wells with inverted subband ordering. In double quantum wells (DQWs), coupling between the layers introduces additional degrees of…
We study the quantum Hall states in the lowest Landau level for a single wide quantum well. Due to a separation of charges to opposite sides of the well, a single wide well can be modelled as an effective two level system. We provide…
Using a recent reformulation of quantum mechanics where the potential function is not required, we are able to obtain the energy spectrum and wave function associated with the infinite square well analytically. Therefore, this work…
We measure the frequency dependent capacitance of a gate covering the edge and part of a two-dimensional electron gas in the quantum Hall regime. In applying a positive gate bias, we create a metallic puddle under the gate surrounded by an…
We use the discrete approach to solve the Schr\"odinger as well as the Bloch equations for a free particle and the quantum gas of free particles embedded in an infinite quantum well with the finite width. We obtain the expressions of energy…
Quantum Wells (QW) are of great importance in optoelectronic devices such as LEDs and LASERs, being the emissive layers.Simulating the quantum particles in different QW topologies like rectangular finite potential wells, multiple potential…
We propose a spin-half approximation method for two-component condensation in double wells to discuss the quantum entanglement of two components. This approximation is presented to be valid under stationary tunneling effect for odd particle…
The eigenvalue equations for the energy of bound states of a particle in a square well are solved, and the exact solutions are obtained, as power series. Accurate analytical approximate solutions are also given. The application of these…
The electronic response of a two-dimensional (2D) electron system represents a key quantity in discussing one-electron properties of electrons in semiconductor heterojunctions, on the surface of liquid helium and in copper-oxide planes of…
Two-dimensional electron and hole gases separated by a few nm from each other are produced in p-i-n diodes based upon MBE-grown GaAs/AlGaAs heterostructures. At such interlayer distances, the exciton formation and possibly Bose-Einstein…
We propose and demonstrate wide-band capacitance measurements on a semiconductor double-quantum dot (DQD) to study tunneling dynamics. By applying phase-tunable high-frequency signals independently to the DQD and a nearby…
Time analysis of oscillations of a particle between wells in the one-dimensional double-well potential with infinite high outside walls, based on wave packet use and energy spectrum analysis, is presented. For the double-well potential of…