Related papers: QuantumFDTD -- A computational framework for the r…
A general method for numerical computation of the thermal density matrix of a single-particle quantum system is presented. The Schrodinger equation in imaginary time tau is solved numerically by the finite difference time domain (FDTD)…
The finite-difference time-domain (FDTD) method is a flexible and powerful technique for rigorously solving Maxwell's equations. However, three-dimensional optical nonlinearity in current commercial and research FDTD softwares requires…
In this paper we start from the Schr\"odinger equation to revisit some classical quantum mechanics from the perspective of phase transition process. Here the relativistic effect of particles moving at high speed can be regarded as the phase…
Quantum theory has been remarkably successful in providing an understanding of physical systems at foundational scales. Solving the Schr\"odinger equation provides full knowledge of all dynamical quantities of the physical system. However…
The main goal of this paper is to set up the coarse-grained formulation of a fractional Schr\"odinger equation that incorporates a higher (spatial) derivative term which accounts for relativistic effects at a lowest order. The corresponding…
Finite-difference time-domain (FDTD) is an effective algorithm for resolving Maxwell equations directly in time domain. Although FDTD has obtained sufficient development, there still exists some improvement space for it, such as…
We present new approaches for solving constrained multicomponent nonlinear Schr\"odinger equations in arbitrary dimensions. The idea is to introduce an artificial time and solve an extended damped second order dynamic system whose…
The Schr\"odingerisation method combined with the autonomozation technique in \cite{cjL23} converts general non-autonomous linear differential equations with non-unitary dynamics into systems of autonomous Schr\"odinger-type equations, via…
A time fractional quantum framework has been introduced into quantum mechanics. A new version of the space-time fractional Schr\"odinger equation has been launched. The introduced space-time fractional Schr\"odinger equation has a new scale…
The energy-based stochastic extension of the Schrodinger equation is a rather special nonlinear stochastic differential equation on Hilbert space, involving a single free parameter, that has been shown to be very useful for modelling the…
We present an application of a nonstandard approximate method---the finite-rank approximation---to solving the time-independent Schr\"odinger equation for a bound-state problem. The method is illustrated on the example of a…
An efficient finite-difference time-domain (FDTD) algorithm is built to solve the transverse electric 2D Maxwell's equations with inhomogeneous dielectric media where the electric fields are discontinuous across the dielectric interface.…
We develop a quantum algorithm for solving high-dimensional fractional Poisson equations. By applying the Caffarelli-Silvestre extension, the $d$-dimensional fractional equation is reformulated as a local partial differential equation in…
We present a formalism based on the functional Schr\"odinger equation to analyse time-dependent tunneling in quantum field theory at the semi-classical level. The full problem is reduced step by step to a finite dimensional quantum…
A covariant non-local extention if the stationary Schr\"odinger equation is presented and it's solution in terms of Heisenbergs's matrix quantum mechanics is proposed. For the special case of the Riesz fractional derivative, the calculation…
The Schr\"odinger-type formalism of the Klein-Gordon quantum mechanics is adapted for the case of the $SL(2,\R)$ spacetime. The free particle case is solved, the results of a recent work are reproduced while all the other, topologically…
We study the Schr\"odinger equation in quantum field theory (QFT) in its functional formulation. In this approach quantum correlation functions can be expressed as classical expectation values over (complex) stochastic processes. We obtain…
A general method has been developed to solve the Schr\"odinger equation for an arbitrary derivative of the $\delta$-function potential in 1-d using cutoff regularization. The work treats both the relativistic and nonrelativistic cases. A…
This article is the second in a series of two presenting the Scale Relativistic approach to non-differentiability in mechanics and its relation to quantum mechanics. Here, we show Schroedinger's equation to be a reformulation of Newton's…
Quantum geometrodynamics (QGD) in extended phase space essentially distinguished from the Wheeler - DeWitt QGD is proposed. The grounds for constructing a new version of quantum geometrodynamics are briefly discussed. The main part in the…