Related papers: Alternative solution to a quantum-mechanical four-…
A new approach to quantum mechanics based on independence of the Continuum Hypothesis is proposed. In one-dimensional case, it is shown that the properties of the set of intermediate cardinality coincide with quantum phenomenology.
In this paper we focus on energy flows in simple quantum systems. This is achieved by concentrating on the quantum Hamilton-Jacobi equation. We show how this equation appears in the standard quantum formalism in essentially three different…
By application of a straightforward variational procedure we derive a simple, analytic upper bound on the ground-state energy eigenvalue of a semirelativistic Hamiltonian for (one or two) spinless particles which experience some…
We consider the equilibria of point particles under the action of two body central forces in which there are both repulsive and attractive interactions, often known as central configurations, with diverse applications in physics, in…
In systems with few degrees of freedom modern quantum calculations are, in general, numerically more efficient than semiclassical methods. However, this situation can be reversed with increasing dimension of the problem. For a…
The purpose of the present note is to propose, in the framework of relativistic quantum mechanics, a new Poincare-invariant equation for two particles with masses m_1, m_2 and spin s_1=s_2=1/2. It is a first-order linear differential…
The quantum dynamical systems of identical particles admitting an additional integral quadratic in momenta are considered. It is found that an appropriate ordering procedure exists which allows to convert the classical integrals into their…
We construct a solution to pentagon equation with anticommuting variables living on two-dimensional faces of tetrahedra. In this solution, matrix coordinates are ascribed to tetrahedron vertices. As matrix multiplication is noncommutative,…
The quantum cosmological version of a nonsingular Universe presented by Mukhanov and Brandenberger in the early nineties has been developed and the Hamilton Jacobi equation has been found under semiclassical (WKB) approximation. It has been…
A crucial problem in quantum cosmology is a careful analysis of the one-loop semiclassical approximation for the wave function of the universe, after an appropriate choice of mixed boundary conditions. The results for Euclidean quantum…
Quantum chemistry is regarded to be one of the first disciplines that will be revolutionized by quantum computing. Although universal quantum computers of practical scale may be years away, various approaches are currently being pursued to…
Using the coordinate transformation method, we solve the one-dimensional Schr\"{o}dinger equation with position-dependent mass(PDM). The explicit expressions for the potentials, energy eigenvalues and eigenfunctions of the systems are…
The plane case of central configurations with four different masses is analyzed theoretically and is computed numerically. We follow Dziobek's approach to four body central configurations with a direct implicit method of our own in which…
We propose a hybrid quantum-classical algorithm for approximating the ground state and ground state energy of a Hamiltonian. Once the Ansatz has been decided, the quantum part of the algorithm involves the calculation of two overlap…
In a stationary case and for any potential, we solve the three-dimensional quantum Hamilton-Jacobi equation in terms of the solutions of the corresponding Schrodinger equation. Then, in the case of separated variables, by requiring that the…
Eigenvalue analysis is widely used for linear instability analysis in both external and internal aerodynamics. It typically involves finding the steady state, linearizing around it to obtain the Jacobian, and then solving for its…
We address the multiplicity of solutions to the time-energy canonical commutation relation for a given Hamiltonian. Specifically, we consider a particle spatially confined in a potential free interval, where it is known that two distinct…
The real Hilbert space formalism developed within the quaternionic quantum mechanics ($\mathbb H$QM) is fully applied to the simple model of the autonomous particle. This framework permits novel insights within the usual description of the…
Quantum mechanics provides several methods to generate and securely distribute private lists of numbers suitably correlated to solve the Three Byzantine Generals Problem. So far, these methods are based on three-qutrit singlet states,…
Four-dimensional mass is determined in four-dimensional pseudo-Euclidean space as a physical invariant of that space. That invariant is discussed as an invariant of electromagnetic type. Finally, equations of Maxwell type are obtained for…