Related papers: General solution of the Schr\"odinger equation
During a continuous measurement, quantum systems can be described by a stochastic Schr\"odinger equation which, in the appropriate limit, reproduces the von Neumann wave-function collapse. The average behavior on the ensemble of all…
We discuss the explicit construction of the Schroedinger equations admitting a representation through some family of general polynomials. Almost all solvable quantum potentials are shown to be generated by this approach. Some generalization…
A supersymmetric technique for the solution of the effective mass Schr\"{o}% dinger equation is proposed. Exact solutions of the Schroedinger equation corresponding to a number of potentials are obtained. The potentials are fully…
Solution of the Schr\"odinger's equation in the zero order WKB approximation is analyzed. We observe and investigate several remarkable features of the WKB$_0$ method. Solution in the whole region is built with the help of simple connection…
The hydrodynamical model of quantum mechanics based on the Schroedinger equation is combined with the magnetohydrodynamical term to form so called quantum magnetohydrodynamic equation. It is shown that the quantum correction to the Alfven…
We review an explicit approach to obtaining numerical solutions of the Schr\"odinger equation that is conceptionally straightforward and capable of significant accuracy and efficiency. The method and its efficacy are illustrated with…
We report on the time dependent solutions of the $q-$generalized Schr\"odinger equation proposed by Nobre et al. [Phys. Rev. Lett. 106, 140601 (2011)]. Here we investigate the case of two free particles and also the case where two particles…
The textbook treatment in that the wave function of a dynamical system is expanded in an eigenfunction series is investigated. With help of an elementary example and some mathematical theorems, it is revealed that in terms of solving the…
Based on the dispersion chain of the Vlasov equations, the paper considers the construction of a new chain of equations of quantum mechanics of high kinematical values. The proposed approach can be applied to consideration of classical and…
One of the greatest scientific achievements of physics in the 20th century is the discovery of quantum mechanics. The Schrodinger equation is the most fundamental equation in quantum mechanics describing the time-based evolution of the…
The basics of the Wigner formulation of Quantum-Mechanics and few related interpretational issues are presented in a simple language. This formulation has extensive applications in Quantum Optics and in Mixed Quantum-Classical formulations.
Using a simple geometrical construction based upon the linear action of the Heisenberg--Weyl group we deduce a new nonlinear Schr\"{o}dinger equation that provides an exact dynamic and energetic model of any classical system whatsoever, be…
We generalize the spherical harmonics for l=1 and give the differential equation that the generalized forms satisfy. The new forms have an obvious interpretation in the context of quantum mechanics.
Quantum computing has emerged as a promising avenue for achieving significant speedup, particularly in large-scale PDE simulations, compared to classical computing. One of the main quantum approaches involves utilizing Hamiltonian…
This study introduces the quantum force wave equation (QFWE) as a general theory of quantum forces, a novel framework that redefines quantum forces as emergent phenomena arising from the interaction between quantum particles and curved…
The study points out that the traditional solutions to wave equation of dissipative wave and motion equation of block for a multi-degree-of-freedom mass spring damper system are the possible solutions, which are not necessarily objective…
We present a phase space formulation of quantum mechanics in the Schr\"odinger representation and derive the associated Weyl pseudo-differential calculus. We prove that the resulting theory is unitarily equivalent to the standard…
In this article we have developed a formalism to obtain the Schr$\ddot{\rm{o}}$dinger equation for a particle in a frame undergoing an uniform acceleration in an otherwise flat Minkowski space-time geometry. We have presented an exact…
In this survey the contemporary results concerning supersymmetries in generalized Schr\"odinger equations are presented. Namely, position dependent mass Sch\"odinger equations are discussed as well as the equations with matrix potentials.…
The generalized Bretherton equation is studied. The classification of the meromorphic traveling wave solutions for this equation is presented. All possible exact solutions of the generalized Brethenton equation are given.