Search results for "Particle in a box"
showing 3 items of 3 documents
On the anomalous Stark effect in a thin disc-shaped quantum dot
2010
The effect of a lateral external electric field F on an exciton ground state in an InAs disc-shaped quantum dot has been studied using a variational method within the effective mass approximation. We consider that the radial dimension of the disc is very large compared to its height. This situation leads to separating the excitonic Hamiltonian into two independent parts: the lateral confinement which corresponds to a two-dimensional harmonic oscillator and an infinite square well in the growth direction. Our calculations show that the complete description of the lateral Stark shift requires both the linear and quadratic terms in F which explains that the exciton possess nonzero lateral dipo…
Lévy flights in an infinite potential well as a hypersingular Fredholm problem.
2016
We study L\'evy flights {{with arbitrary index $0< \mu \leq 2$}} inside a potential well of infinite depth. Such problem appears in many physical systems ranging from stochastic interfaces to fracture dynamics and multifractality in disordered quantum systems. The major technical tool is a transformation of the eigenvalue problem for initial fractional Schr\"odinger equation into that for Fredholm integral equation with hypersingular kernel. The latter equation is then solved by means of expansion over the complete set of orthogonal functions in the domain $D$, reducing the problem to the spectrum of a matrix of infinite dimensions. The eigenvalues and eigenfunctions are then obtained numer…
A Graph-Theoretical Approach to Calculate Vibrational Energies of Atomic and Subatomic Systems
2012
One of the challenges still pending in string theory and other particle physics related fields is the accurate prediction of the masses of the elementary particles defined in the standard model. In this paper an original algorithm to assign graphs to each of these particles is proposed. Based on this mapping, we demonstrate that certain indices associated with the topology of the graph (graph theoretical indices) are very effective in predicting the masses of the particles. Specifically, the spectral moments of the graph adjacency matrix weighted by edge degrees play a key role in the excellent correlations found. Moreover, the same topological pattern is found in other well known quantum s…