Results 1 
3 of
3
Nonstandard Feynman path integral for harmonic oscillator
 J. Math. Phys
, 1999
"... Abstract. Using Nonstandard Analysis, we will provide a rigorous computation for the harmonic oscillator Feynman path integral. The computation will be done without having prior knowledge of the classical path. We will see that properties of classical physics falls out naturally from a purely quantu ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Abstract. Using Nonstandard Analysis, we will provide a rigorous computation for the harmonic oscillator Feynman path integral. The computation will be done without having prior knowledge of the classical path. We will see that properties of classical physics falls out naturally from a purely quantum mechanical point of view. We will assume that the reader is familiar with Nonstandard Analysis. I. Introduction. In quantum mechanics, we are interested in finding the wave function which satisfies Schrodinger’s equation. Equivalently, we can find the propagator or integral kernel K(q, q0, t) which satisfies
algorithm proposed
, 2005
"... The goals of this paper are to show the following. First, Grover’s algorithm can be viewed as a digital approximation to the analog quantum ..."
Abstract
 Add to MetaCart
The goals of this paper are to show the following. First, Grover’s algorithm can be viewed as a digital approximation to the analog quantum
Abstract
, 805
"... General stochastic dynamics, developed in a framework of Feynman path integrals, have been applied to Lewinian field–theoretic psychodynamics [1,2,13], resulting in the development of a new concept of life–space foam (LSF) as a natural medium for motivational and cognitive psychodynamics. According ..."
Abstract
 Add to MetaCart
General stochastic dynamics, developed in a framework of Feynman path integrals, have been applied to Lewinian field–theoretic psychodynamics [1,2,13], resulting in the development of a new concept of life–space foam (LSF) as a natural medium for motivational and cognitive psychodynamics. According to LSF formalisms, the classic Lewinian life space can be macroscopically represented as a smooth manifold with steady force–fields and behavioral paths, while at the microscopic level it is more realistically represented as a collection of wildly fluctuating force–fields, (loco)motion paths and local geometries (and topologies with holes). A set of least– action principles is used to model the smoothness of global, macro–level LSF paths, fields and geometry. To model the corresponding local, micro–level LSF structures, an adaptive path integral is used, defining a multi–phase and multi–path (multi– field and multi–geometry) transition process from intention to goal–driven action. Application examples of this new approach include (but are not limited to) information processing, motivational fatigue, learning, memory and decision–making.