Related papers: The Infinite Square Well Is Subtle
A representation formula for the solution of the $\infty$-Laplace equation is constructed in a punctured square, the prescribed boundary values being $u=0$ on the sides and $u=1$ at the centre. This so-called $\infty$-potential is obtained…
We use an one dimensional model of a square barrier embedded in an infinite potential well to demonstrate that tunneling leads to a complex behavior of the wave function and that the degree of complexity may be quantified by use of the…
The article considers Chaplygin sleigh on a plane in potential well, assuming that an external potential force is supplied at the mass center. Two particular cases are studied in some detail, namely, a one-dimensional potential valley and a…
We analyze possible motion control of microparticles by means of external electromagnetic fields which induce potential wells having fixed spatial distribution but deepening over time up to some limit. It is assumed that given particles are…
We present one dimensional potentials $V(x)= V_0[e^{2|x|/a}-1]$ as solvable models of a well $(V_0>0)$ and a barrier ($V_0<0$). Apart from being new addition to solvable models, these models are instructive for finding bound and scattering…
Eigenstates of a particle in a localized and unconfined harmonic potential well are investigated. Effects due to the variation of the potential parameters as well as certain results from asymptotic expansions are discussed.
In this paper an iterative minimization method is proposed to approximate the minimizer to the double-well energy functional arising in the phase-field theory. The method is based on a quadratic functional posed over a nonempty closed…
We point out that a non-overlapping well (at negative energies) adjacent to a finite barrier (at positive energies) is a simple potential which is generally missed out while discussing the one-dimensional potentials in the textbooks of…
The main goal of this work is to solve the nonrelativistic wave equation for a new potential configuration that describes the quantum states of a particle that lies within a onedimensional infinite well of width L using the Asymptotic…
Following a recently proposed confinement generating mechanism, we provide a new string inspired model with a massive dilaton and a new dilaton coupling function [5]. By solving analytically the equations of motion, a new class of confining…
The phase diagram of the penetrable square-well fluid is investigated through Monte Carlo simulations of various nature. This model was proposed as the simplest possibility of combining bounded repulsions at short scale and short-range…
A square potential well with position-dependent mass is studied for bound states. Applying appropriate matching conditions, a transcendental equation is derived for the energy eigenvalues. Numerical results are presented graphically and the…
Continuing our investigation into the numerical properties of the Hierarchical Reference Theory, we study the square well fluid of range lambda from slightly above unity up to 3.6. After briefly touching upon the core condition and the…
Hydrodynamic equations for ideal incompressible fluid are written in terms of generalized stream function. Two-dimensional version of these equations is transformed to the form of one dynamic equation for the stream function. This equation…
Perfectly conducting boundaries, and their Dirichlet counterparts for quantum scalar fields, predict nonintegrable energy densities. A more realistic model with a finite ultraviolet cutoff yields two inconsistent values for the force on a…
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…
By means of a suitable rational approximation to the logarithmic derivative of the wavefunction we obtain tight upper and lower bounds to the eigenvalues and critical parameters of the quartic double-well potential.
The "particle in a box" problem is investigated for a relativistic particle obeying the Klein-Gordon equation. To find the bound states, the standard methods known from elementary non-relativistic quantum mechanics can only be employed for…
We show in spatially one dimensional Madelung fluid that a simple requirement on local stability of the maximum of quantum probability density will, if combined with the global scale invariance of quantum potential, lead to a class of…
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…