Related papers: QuantumFDTD -- A computational framework for the r…
Using closed positive extensions of the quadratic form in the potential term we provide alternative solutions to the eigenstate equation for the free quantum field Hamiltonian in the Schr\"o\-din\-ger representation. We show that admissible…
The Dirac equation is solved using three-dimensional Finite Difference-Time Domain (FDTD) method. $Zitterbewegung$ and the dynamics of a well-localized electron are used as examples of FDTD application to the case of free electrons.
In this work, we apply the Cole's non-standard form of the FDTD to solve the time dependent Schr\"odinger equation. We deduce the equations for the non-standard FDTD considering an electronic wave function in the presence of potentials…
This paper is about the fractional Schr\"odinger equation expressed in terms of the Caputo time-fractional and quantum Riesz-Feller space fractional derivatives for particle moving in a potential field. The cases of free particle (zero…
We consider the $1d$ cubic nonlinear Schr\"odinger equation with an external potential $V$ that is non-generic. Without making any parity assumption on the data, but assuming that the zero energy resonance of the associated Schr\"odinger…
We propose a numerical algorithm that integrates quantum two-level systems (TLSs) into the finite-difference time-domain (FDTD) framework for simulating quantum emitters in arbitrary 3D photonic environments. Conventional methods struggle…
We introduce a numerical method for the solution of the time-dependent Schrodinger equation with a smooth potential, based on its reformulation as a Volterra integral equation. We present versions of the method both for periodic boundary…
We consider the Schr\"odinger equation for a relativistic point particle in an external 1-dimensional $\delta$-function potential. Using dimensional regularization, we investigate both bound and scattering states, and we obtain results that…
We present Fiend - a simulation package for three-dimensional single-particle time-dependent Schr\"odinger equation for cylindrically symmetric systems. Fiend has been designed for the simulation of electron dynamics under inhomogeneus…
We study the probability and energy conservation properties of a leap-frog finite-difference time-domain (FDTD) method for solving the Schr\"odinger equation. We propose expressions for the total numerical probability and energy contained…
A global solution of the Schr\"odinger equation for explicitly time-dependent Hamiltonians is derived by integrating the non-linear differential equation associated with the time-dependent wave operator. A fast iterative solution method is…
In these lectures, we discuss different types of renormalization problems in QCD and their non-perturbative solution in the framework of the lattice formulation. In particular the recursive finite size methods to compute the…
This paper introduces a new computational framework to derive electromagnetic field derivatives with respect to multiple design parameters up to any order with the Finite-Difference Time-Domain (FDTD) technique. Specifically, only one FDTD…
It is not possible, using standard lattice techniques in Euclidean space, to calculate the complete fermionic spectrum of a quantum field theory. Algorithms running on quantum computers have the potential to access the theory with real-time…
By their very nature, field-theoretical Hamiltonians are derived in momentum representation. To solve the corresponding integro-differential equations is more difficult than to solve the simpler differential equations in configuration space…
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…
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…
We present a code for solving the single-particle, time-independent Schr\"odinger equation in two dimensions. Our program utilizes the imaginary time propagation (ITP) algorithm, and it includes the most recent developments in the ITP…
Employing the phase-space representation of second order ordinary differential equations we developed a method to find the eigenvalues and eigenfunctions of the 1-dimensional time independent Schr\"odinger equation for quantum model…
We consider relativistic quantum field theory in the presence of an external electric potential in a general curved space-time geometry. We utilise Fermi coordinates adapted to the time-like geodesic to describe the low-energy physics in…