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The Feynman Integral
, 2008
"... In 1922 Norbert Wiener [I], treating the Brownian motion of a particle, introduced a measure on the space of continuous real functions, and a corresponding integral. In 1948 Richard Feynman [2], studying the quantum mechanics of a particle, introduced a different integral over the same space. He a ..."
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Cited by 4 (1 self)
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In 1922 Norbert Wiener [I], treating the Brownian motion of a particle, introduced a measure on the space of continuous real functions, and a corresponding integral. In 1948 Richard Feynman [2], studying the quantum mechanics of a particle, introduced a different integral over the same space. He also showed that his integral can be used to represent the solution of the initial value
Feynman Integrals for a Class of Exponentially Growing Potentials
, 1997
"... We construct the Feynman integrands for a class of exponentially growing timedependent potentials as white noise functionals. We show that they solve the Schrodinger equation. The Morse potential is considered as a special case. Contents 1 Introduction 3 2 White noise analysis 4 3 The free Feynma ..."
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We construct the Feynman integrands for a class of exponentially growing timedependent potentials as white noise functionals. We show that they solve the Schrodinger equation. The Morse potential is considered as a special case. Contents 1 Introduction 3 2 White noise analysis 4 3 The free Feynman integrand 8 4 The Feynman integrand for a new class of unbounded potentials 10 4.1 The interactions . . . . . . . . . . . . . . . . . . . . . . . . . . 10 4.2 The Feynman integrand as a generalized white noise functional 11 4.3 Schrodinger equation . . . . . . . . . . . . . . . . . . . . . . . 15 4.4 Continuation to imaginary mass . . . . . . . . . . . . . . . . . 18 4.5 Timedependent potentials . . . . . . . . . . . . . . . . . . . . 21 5 A special case: The Morse Potential 23 References 26 1 Introduction As an alternative approach to quantum mechanics Feynman introduced the concept of path integrals, see [FeHi65], which developed into an extremely useful tool in many branches of t...
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
PRODUCT FORMULA FOR RESOLVENTS OF NORMAL OPERATORS AND THE MODIFIED FEYNMAN INTEGRAL
"... you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact inform ..."
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Cited by 3 (0 self)
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you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your personal, noncommercial use. Please contact the publisher regarding any further use of this work. Publisher contact information may be obtained at
Outline ◮ The Physical Setting ◮ The Goal ◮ One Result ◮ The Main Ideas Leading to the Results
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The Feynman Path Integral: An Historical Slice
, 2003
"... Efforts to give an improved mathematical meaning to Feynman’s path integral formulation of quantum mechanics started soon after its introduction and continue to this day. In the present paper, one common thread of development is followed over many years, with contributions made by various authors. T ..."
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Efforts to give an improved mathematical meaning to Feynman’s path integral formulation of quantum mechanics started soon after its introduction and continue to this day. In the present paper, one common thread of development is followed over many years, with contributions made by various authors. The present version of this line of development involves a continuoustime regularization for a general phase space path integral and provides, in the author’s opinion at least, perhaps the optimal formulation of the path integral. The Feynman Path Integral, 1948 Much has already been written about Feynman path integrals, and, no doubt, much more will be written in the future. A comprehensive survey after more than fifty years since their introduction would be a major undertaking, and this paper is not such a survey. Rather, it is an attempt to follow one relatively narrow development regarding a special form of regularization used in the definition of path integrals. Since we deal with several different approaches, this paper does not go too deeply into any one of them; it is intended more as a conceptual overview rather than a detailed exposition. Electronic mail:
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
FEYNMAN INTEGRALS AS HIDA DISTRIBUTIONS: THE CASE OF NONPERTURBATIVE POTENTIALS DEDICATED TO JEANMICHEL BISMUT AS A SMALL TOKEN OF APPRECIATION
, 805
"... Feynman ”integrals”, such as J = d ∞ ( ∫ t ..."