Related papers: Special rectangular (double-well and hole) potenti…
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 consider a particle in a one-dimensional box of length $L$ with a Maxwell bath at one end and a reflecting wall at the other end. Using a renewal approach, as well as directly solving the master equation, we show that the system exhibits…
An infinite sequence of potential well functions is considered. A numerical method is used for the Schr$\ddot{\text{o}}$dinger equation to obtain the energy eigenvalue spectra for a number of these potential well functions. The results for…
We study the dynamics of isolated closed domain walls with 3+1 numerical relativity. A closed wall shrinks due to its own surface tension, and its surface energy is converted to the kinetic energy, leading to implosion. Then, it can result…
The double well potential is arguably one of the most important potentials in quantum mechanics, because the solution contains the notion of a state as a linear superposition of `classical' states, a concept which has become very important…
We propose to experimentally realize an odd parity eigenstate $\left\vert b\right\rangle $ of two atoms in the double well. The occupation probability of this state shows evident dependence on the interaction, distinct from the result of…
We study the ground state for many interacting bosons in a double-well potential, in a joint limit where the particle number and the distance between the potential wells both go to infinity. Two single-particle orbitals (one for each well)…
We propose an experiential formula for the calculation of the energy eigenvalues of a particle moving in a one-dimension finite-deep square well potential after some physical considerations. This formula shows a simple relation between the…
Rotating black holes are algebraically special solutions to the vacuum Einstein equation. Using properties of the algebraically special solutions we construct the dual fluid, which flows on black hole horizon. An explicit form of the Kerr…
Particles with negative energies are considered for three different cases: inside of horizon of Schwarzschild black hole, Milne's coordinates in flat Minkowski space-time (Milne's universe using nonsynchronous coordinates) and in…
In this article, we study scaling laws for singularly perturbed two-well energies with prescribed Dirichlet boundary data in settings where the wells and/or the boundary data are incompatible. Our main focus is the geometrically linear…
The paper wishes to demonstrate that, in quantum systems with boundaries, different boundary conditions can lead to remarkably different physical behaviour. Our seemingly innocent setting is a one dimensional potential well that is divided…
This article examines the suggestion made in Ref. [EPL, 115 (2016) 60001] that a solution to a particle in an infinite spherical well model, if it is square-integrable, is a physically valid solution, even if at the precise location of the…
In paper approach of double complex SUSY-transformations with not coincident complex energies of transformation is developed, allowing to deform given real potential $V_{1}$ with obtaining exact solutions. The explicit solutions of the…
Analytic and approximate solutions for the energy eigenvalues generated by the hyperbolic potentials $V_m(x)=-U_0\sinh^{2m}(x/d)/\cosh^{2m+2}(x/d),\,m=0,1,2,\dots$ are constructed. A byproduct of this work is the construction of polynomial…
A method for determination of bound state energies for an asymmetric quantum well with an arbitrary shape of the bottom is suggested. It is shown that how the equation determining the energy levels can be easily derived if one knows the…
We present a class of confining potentials which allow one to reduce the one-dimensional Schroodinger equation to a named equation of mathematical physics, namely either Bessel's or Whittaker's differential equation. In all cases, we…
The recent observation that black holes in certain Einstein-Maxwell-Dilaton (EMD) theories can violate the entropy super-additivity led to the suggestion that these black holes might repel each other. In this paper, we consider EMD theories…
We study the energy properties of a particle in one dimensional semi-harmonic rectangular wells and barriers. The integration of energies is obtained by solving a simple transcendental equation. Scattering states are shown to include cases…
The original model of the infinite square well contains a vague notation infinity and therefore results some ambiguities. We investigate to obtain a functional form for the potential energy V(x). This is done by substituting back the…