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A Rigorous Real Time Feynman Path Integral and Propagator
 J. Phys. A: Math. Gen
"... This work partially fulfills the author’s Ph.D. thesis requirements ..."
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This work partially fulfills the author’s Ph.D. thesis requirements
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 ..."
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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
A Functional Integral Representation for Many Boson Systems I: The Partition Function
"... Abstract. We derive a functional integral representation for the partition function of a We are developing a set of tools and techniques for analyzing the large distance/infrared behaviour of a system of identical bosons, as the temperature tends to zero. The total energy of the many boson systems c ..."
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Abstract. We derive a functional integral representation for the partition function of a We are developing a set of tools and techniques for analyzing the large distance/infrared behaviour of a system of identical bosons, as the temperature tends to zero. The total energy of the many boson systems considered in this paper has two sources. First, each particle in the system has a kinetic energy. We shall denote the corresponding
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 ..."
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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
CERTIFICATE OF APPROVAL
, 2014
"... Path integration with nonpositive distributions and applications to the Schrödinger equation ..."
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Path integration with nonpositive distributions and applications to the Schrödinger equation