Related papers: The quantum Gaussian well
A simple decay model is introduced. The model comprises of a point potential well, which experiences an abrupt change. Due to the temporal variation the initial quantum state can either escape from the well or stay localized as a new bound…
Quantum mechanics has introduced a new theoretical framework for the study of molecules, enabling the prediction of properties and dynamics through the solution of the Schr\"odinger equation applied to these systems. However, solving this…
We explore the quantum nature of black holes by introducing an effective framework that takes into account deviations from the classical results. The approach is based on introducing quantum corrections to the classical Schwarzschild…
The notion of a double well potential typically involves two regions of space separated by a repulsive potential barrier. The solution is a wave function that is suppressed in the barrier region and localized in the two surrounding regions.…
In this paper, we sketch and emphasize the automatic emergence of a quantum potential (QP) in general Hamilton-Jacobi equation via commuting relations, quantum canonical transformations and without the straight effect of wave function. The…
We describe an example of an exact, quantitative Jeopardy-type quantum mechanics problem. This problem type is based on the conditions in one-dimensional quantum systems that allow an energy eigenstate for the infinite square well to have…
A variational method is discussed, extending the Gaussian effective potential to higher orders. The single variational parameter is replaced by trial unknown two-point functions, with infinite variational parameters to be optimized by the…
A quantization procedure, which has recently been introduced for the analysis of Painlev\'e equations, is applied to a general time-independent potential of a Newton equation. This analysis shows that the quantization procedure preserves…
Previously we found a unique quantum system with a positive gauge-invariant Weyl-Stratonovich quasi-probability density function which can be defined by the so-called {\guillemotleft}quadratic funnel{\guillemotright} potential [Phys. Rev. A…
A stochastic model for the continuous nondemolition ohservation of the position of a quantum particle in a potential field and a boson reservoir is given. lt is shown that any Gaussian wave function evolving according to the posterior wave…
The energy-based stochastic extension of the Schrodinger equation is perhaps the simplest mathematically rigourous and physically plausible model for the reduction of the wave function. In this article we apply a new simulation methodology…
Quantum tunneling between two potential wells in a magnetic field can be strongly increased when the potential barrier varies in the direction perpendicular to the line connecting the two wells and remains constant along this line. A…
We show that given a suitable but essentially arbitrary function Q(x,t,h) there are "generalized" quantum theories having Q as a quantum potential.
A Gaussian resolution method for the computation of equilibrium density matrices rho(T) for a general multidimensional quantum problem is presented. The variational principle applied to the ``imaginary time'' Schroedinger equation provides…
We survey various origins and expressions for the quantum potential with some new observations.
We present a simple method to deal with caustics in the semiclassical approximation to the partition function of a one-dimensional quantum system. The procedure, which makes use of complex trajectories, is applied to the quartic double-well…
The classical square well potential is smoothed with a finite range smoothing function in order to get a new simple strictly finite range form for the phenomenological nuclear potential. The smoothed square well form becomes exactly zero…
Liouville transformations map in a rigorous manner one Schr\"odinger equation into another, with a changed scattering potential. They are used here to transform quantum reflection of an atom on an attractive well into reflection of the atom…
We analyse the accuracy of the approximate WKB quantization for the case of general one-dimensional quartic potential. In particular, we are interested in the validity of semiclassically predicted energy eigenvalues when approaching the…
A Wronskian determinant approach is suggested to study the energy and the wave function for one-dimensional Schrodinger equation. An integral equation and the corresponding Green's function are constructed. As an example, we employed this…