arXiv subjects
Publications and source records attributed to Werner Westerkamp.
We construct the Feynman integrands for a class of exponentially growing time-dependent potentials as white noise functionals. We show that they solve the Schroedinger equation. The Morse potential is considered as a special case.
We discuss Donsker's delta function within the framework of White Noise Analysis, in particular its extension to complex arguments. With a view towards applications to quantum physics we also study sums and products of Donsker's delta functions.
We review some basic notions and results of White Noise Analysis that are used in the construction of the Feynman integrand as a generalized White Noise functional. After sketching this construction for a large class of potentials we show that the resulting Feynman integrals solve the Schroedinger equation.
We review some basic notions and results of White Noise Analysis that are used in the construction of the Feynman integrand as a generalized White Noise functional. We show that the Feynman integrand for the harmonic oscillator in an external potential is a Hida distribution.
The first part of this thesis proposes a general approach to infinite dimensional non-Gaussian analysis, including the Poissonian case. In particular distribution theory is developed. Using appropriate integral transformations, generalized and test functionals are characterized in terms of holomorphy. Furthermore differential operators, Wick product and change of measure are discussed. In the second part the Gaussian case (White Noise Analysis) is worked out in more detail. Furthermore operators on distribution spaces e.g. compositions with shifts and complex scaling are discussed. In the third part Feynman integrals are constructed using White Noise distributions as integrands. Its expectation yields the path integral. This rigorous approach is applied to the interacting case. A generalization of the Khandekar Streit method is proposed. The resulting class of admissible potentials covers signed measures. The Albeverio Hoegh-Krohn class, which consists of Fourier transforms of measures, is discussed. The third approach is based on complex scaling. The so-called Doss class allows analytic potentials which obey some growth condition. Using the White Noise calculus of differential operators, the functional form of the canonical commutation relation is derived. Finally Ehrenfest's theorem is proven.
We give a general approach to infinite dimensional non-Gaussian Analysis for measures which need not have a logarithmic derivative. This framework also includes the possibility to handle measures of Poisson type.
We describe positive generalized functionals in Gaussian Analysis. We focus on distribution spaces larger than the space of Hida Distributions. It is shown that a positive distribution is represented by a measure with specific growth of its moments. Equivalently this may be replaced by an integrability condition.