相关论文: Efficient Simulation of Quantum State Reduction

A method of solving the time-dependent Schr\"odinger equation is presented, in which a finite region of space is treated explicitly, with the boundary conditions for matching the wave-functions on to the rest of the system replaced by an…

An adapted representation of quantum mechanics sheds new light on the relationship between quantum states and classical states. In this approach the space of quantum states splits into a product of the state space of classical mechanics and…

We present simulations of non-equilibrium dynamics of quantum field theories on digital quantum computers. As a representative example, we consider the Schwinger model, a 1+1 dimensional U(1) gauge theory, coupled through a Yukawa-type…

A general class of discrete unitary models are described whose behavior in the continuum limit corresponds to a many-body Schrodinger equation. On a quantum computer, these models could be used to simulate quantum many-body systems with an…

Given a spatially dependent mass distribution we obtain potential functions for exactly solvable nonrelativistic problems. The energy spectrum of the bound states and their wavefunctions are written down explicitly. This is accomplished by…

Solving the time-dependent Schr\"odinger equation (TDSE) is pivotal for modeling non-adiabatic electron dynamics, a key process in ultrafast spectroscopy and laser-matter interactions. However, exact solutions to the TDSE remain…

We analyze the non-Markovian stochastic Schroedinger equation describing a particle subject to spontaneous collapses in space (in the language of collapse models), or subject to a continuous measurement of its position (in the language of…

A new discrete model for energy relaxation of a quantum particle is described via a projection operator, causing the wave function collapse. Power laws for the evolution of the particle coordinate and momentum dispersions are derived. A new…

The projection formalism for calculating effective Hamiltonians and resonances is generalized to the nonlocal and/or nonhermitian case, so that it is applicable to the reduction of relativistic systems (Bethe-Salpeter equations), and to…

It is known that the Schroedinger equation may be derived from a hydrodynamic model in which the Lagrangian position coordinates of a continuum of particles represent the quantum state. Using Routh\s method of ignorable coordinates it is…

The Schrodinger equation for stationary states is studied in a central potential V(r) proportional to the inverse power of r of degree beta in an arbitrary number of spatial dimensions. The presence of a single term in the potential makes…

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 intrinsic and dynamic kinetic energies, and the potential energies of electron states in the hydrogen atom, were determined using the operator formalism in the Schrodinger nonrelativistic equation. Intrinsic energies were determined…

We propose an explicit, oracle-free quantum framework for numerically simulating general linear partial differential equations (PDEs), extending previous work to incorporate (a) Robin boundary conditions - which include Neumann and…

We discuss Staruszkiewicz's nonlinear modification of the Schr\"{o}dinger equation. It is pointed out that the expression for the energy functional for this modification is not unique as the field-theoretical definition of energy does not…

This paper is devoted to the well-posedness of stochastic nonlinear Schr\"odinger equations in the energy space H1(Rd), which is a natural continuation of our recent work [1]. We consider both focusing and defocusing nonlinearities and…

Convergence conditions for quantum annealing are derived for optimization problems represented by the Ising model of a general form. Quantum fluctuations are introduced as a transverse field and/or transverse ferromagnetic interactions, and…

A central aim of physics is to describe the dynamics of physical systems. Schrodinger's equation does this for isolated quantum systems. Describing the time evolution of a quantum system that interacts with its environment, in its most…

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…

Energy diffusion due to spontaneous localization (SL) for a relativistically-fast moving particle is examined. SL is an alternative to standard quantum theory in which quantum state reduction is treated as a random physical process which is…