Space-Time Approach to Non-Relativistic Quantum Mechanics
Reads0
Chats0
TLDR
In this paper, the authors formulated non-relativistic quantum mechanics in a different way and showed that the probability of an event which can happen in several different ways is the absolute square of a sum of complex contributions, one from each alternative way.Abstract:
Non-relativistic quantum mechanics is formulated here in a different way. It is, however, mathematically equivalent to the familiar formulation. In quantum mechanics the probability of an event which can happen in several different ways is the absolute square of a sum of complex contributions, one from each alternative way. The probability that a particle will be found to have a path x(t) lying somewhere within a region of space time is the square of a sum of contributions, one from each path in the region. The contribution from a single path is postulated to be an exponential whose (imaginary) phase is the classical action (in units of ℏ) for the path in question. The total contribution from all paths reaching x, t from the past is the wave function ψ(x, t). This is shown to satisfy Schroedinger's equation. The relation to matrix and operator algebra is discussed. Applications are indicated, in particular to eliminate the coordinates of the field oscillators from the equations of quantum electrodynamics.read more
Citations
More filters
Journal ArticleDOI
Computationally efficient molecular dynamics integrators with improved sampling accuracy
Cristian Predescu,Ross A. Lippert,Michael P. Eastwood,Douglas J. Ierardi,Huafeng Xu,Morten Ø. Jensen,Kevin J. Bowers,Justin Gullingsrud,C. A. Rendleman,Ron O. Dror,David E. Shaw +10 more
TL;DR: This work introduces a class of explicit variational integrators designed to achieve high accuracy for quadratic potentials, with little additional computation relative to traditional integrators, and shows that they improve accuracy for classical biomolecular simulations.
INVITED ARTICLE Path integral renormalization for quantum dissipative dynamics with multiple timescales
TL;DR: In this paper, an iterative path integral methodology that involves a propagator tensor, whose rank is roughly equal to the number of time steps that span the bath-induced memory is presented.
Journal ArticleDOI
Macroscopic quantum tunneling and quantum-classical phase transitions of the escape rate in large spin systems
S. A. Owerre,Manu B. Paranjape +1 more
TL;DR: In this paper, the authors present a review on the theoretical and experimental developments on macroscopic quantum tunneling and quantum-classical phase transitions of the escape rate in large spin systems.
Journal ArticleDOI
Quantum Monte Carlo simulations of selected ammonia clusters (n = 2-5): isotope effects on the ground state of typical hydrogen bonded systems.
E. Curotto,Massimo Mella +1 more
TL;DR: This work compares the energy obtained from path integral simulations at several low temperatures with those obtained by diffusion Monte Carlo, for two dimers, and finds that at 4 K, the fully deuterated dimer energy is in excellent agreement with the ground state energy of the same.