相关论文: A method for classical and quantum mechanics

Quantum annealing (QA) has the potential to significantly improve solution quality and reduce time complexity in solving combinatorial optimization problems compared to classical optimization methods. However, due to the limited number of…

It is first shown that when the Schr\"{o}dinger equation for a wave function is written in the polar form, complete information about the system's {\em quantum-ness} is separated out in a single term $Q$, the so called `quantum potential'.…

As a model for the semiclassical analysis of quantum-mechanical systems with both potentials and boundary conditions, we construct the WKB propagator for a linear potential sloping away from an impenetrable boundary. First, we find all…

We study the dynamics of classical and quantum systems undergoing a continuous measurement of position by schematizing the measurement apparatus with an infinite set of harmonic oscillators at finite temperature linearly coupled to the…

We describe a quantum perturbative approach to evaluating the phase shift of an atom interferometer in a weakly anharmonic trap. This provides a simple way to evaluate quantum corrections to the standard semi-classical approximation. The…

An elementary introduction is given to the subject of Supersymmetry in Quantum Mechanics. We demonstrate with explicit examples that given a solvable problem in quantum mechanics with n bound states, one can construct new exactly solvable n…

The oscillator representation method is presented and used to calculate the energy spectra for a superposition of Coulomb and power-law potentials and for Coulomb and Yukawa potentials. The method provides an efficient way to obtain…

We show that the recently discovered quantum-enhanced measurement protocol of coherent averaging that is capable of achieving Heisenberg-limited sensitivity without using entanglement, has a classical analogue. The classical protocol uses N…

Developing a quantum analog of the modern classical theory of causation, as formulated by Pearl and others using directed acyclic graphs, requires a theory of random or stochastic time development at the microscopic level, where the…

A simple method has been introduced to furnish the equilibrium solution of the Wigner equation for all order of the quantum correction. This process builds up a recursion relation involving the coefficients of the different power of the…

Quantum sensing harnesses the unique properties of quantum systems to enable precision measurements of physical quantities such as time, magnetic and electric fields, acceleration, and gravitational gradients well beyond the limits of…

This paper is an application of the ideas of the Born-Oppenheimer (or slow/fast) approximation in molecular physics and of the Isaacson (or short-wave) approximation in classical gravity to the canonical quantization of a perturbed…

In a previous paper (J. Phys. A 36, 11807 (2003)), we introduced the `asymptotic iteration method' for solving second-order homogeneous linear differential equations. In this paper, we study perturbed problems in quantum mechanics and we…

We present a practical implementation of the perturbation theory derived by Lynden-Bell (2015) for describing, to arbitrary precision, the orbit of a particle in an arbitrary spherically-symmetric potential. Our implementation corrects…

Approximation algorithms for classical constraint satisfaction problems are one of the main research areas in theoretical computer science. Here we define a natural approximation version of the QMA-complete local Hamiltonian problem and…

This paper is a generalization of previous work on the use of classical canonical transformations to evaluate Hamiltonian path integrals for quantum mechanical systems. Relevant aspects of the Hamiltonian path integral and its measure are…

We introduce a non perturbative general approximation scheme (NGAS) that can handle interactions of any strength in quantum theory. This approach starts with an input Hamiltonian that can be solved exactly. The interaction effects are then…

In this paper, I present a mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, it is demonstrated that quantum tunneling can be…

In a first part we study the phi^{p+1}--field theory from the classical point of view. Using Butcher series we compute explicitly the perturbative expansion of the solutions and we prove that this expansion converges if the coupling…

We define a class of quantum systems called regular quantum graphs. Although their dynamics is chaotic in the classical limit with positive topological entropy, the spectrum of regular quantum graphs is explicitly computable analytically…