Related papers: Spherical quantum well
The angular part of the Faddeev equations is solved analytically for s-states for two-body square-well potentials. The results are, still analytically, generalized to arbitrary short-range potentials for both small and large distances. We…
In spherical symmetry compelling numerical evidence suggests that in general relativity solutions near the threshold of black hole formation exhibit critical behavior. One aspect of this is that threshold solutions themselves are…
Using mainly two techniques, a point transformation and a time dependent supersymmetry, we construct in sequence several quantum infinite potential wells with a moving barrier. We depart from the well known system of a one-dimensional…
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.
We study the bound-state solutions of vanishing angular momentum in a quaternionic spherical square-well potential of finite depth. As in the standard quantum mechanics, such solutions occur for discrete values of energies. At first glance,…
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.…
The quantization of a spherically symmetric null shells is performed and extended to the framework of phase-space noncommutative (NC) quantum mechanics. The encountered properties are investigated making use of the Israel junction…
The structure of the energy levels in a deep triple well is analyzed using simple quantum mechanical considerations. The resultant spectra of the first three energy levels are found to be composed of a ground state localized at the central…
Recently, Theophilou (J. Chem.Phys {\bf 149} 074104 (2018)) showed that a set of spherically symmetric densities determines uniquely the external potential in molecules and solids. Here, spherically symmetric Kohn-Sham-like equations 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…
We compare the classical and quantum mechanical position-space probability densities for a particle in an asymmetric infinite well. In an idealized system with a discontinuous step in the middle of the well, the classical and quantum…
Consider the semiclassical limit, as the Planck constant $\hbar\ri 0$, of bound states of a one-dimensional quantum particle in multiple potential wells separated by barriers. We show that, for each eigenvalue of the Schr\"odinger operator,…
In this study, we have investigated the inter-sublevel optical properties of a core/shell/well/shell spherical quantum dot with the form of quantum dot-quantum well heterostructure. In order to determine the energy eigenvalues and…
A method is described by which a function defined on a cubic grid (as from a finite difference solution of a partial differential equation) can be resolved into spherical harmonic components at some fixed radius. This has applications to…
Isolated horizon conditions specialized to spherical symmetry can be imposed directly at the quantum level. This answers several questions concerning horizon degrees of freedom, which are seen to be related to orientation, and its…
Spherical means are well-known useful tool in the theory of partial differential equations with applications to solving hyperbolic and ultrahyperbolic equations and problems of integral geometry, tomography and Radon transforms. We…
One examines the infinitely deep quantum cavity, also known as the quantum infinite square well, within the framework of the real Hilbert space. The solutions are considered in terms of complex wave functions, and also in terms of…
The accuracy of the WKB approximation when predicting the energy splitting of bound states in a double well potential is the main subject of this paper. The splitting of almost degenerate energy levels below the top of the barrier results…
In this paper, the principles of the general relativity are used to formulate quantum wave equations for spin-0 and spin-1/2 particles. More specifically, the equations are worked in a Schwarzschild-like metric. As a test, the hydrogen atom…
In this paper, a 1-parameter family of Newton's equivalent Hamiltonians (NEH) for finite square well potential is analyzed in order to obtain bound state energy spectrum and wavefunctions. For a generic potential, each of the NEH is…