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Journal of Physics Conference Series

The growth and zeros of Bargmann functions

Apostol Vourdas

Published Mar 1, 2010• 1 citation
Publisher

Abstract

The Bargmann formalism is presented with emphasis on the growth and zeros of Bargmann functions. Hadamard's theorem is expressed in a physical language and it is used to construct quantum states, with given zeros in their Bargmann function. Various examples are discussed. The time evolution of Bargmann functions and the motion of their zeros, for various Hamiltonians, is studied.

DOI
10.1088/1742-6596/213/1/012001

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The Bargmann formalism is presented with emphasis on the growth and zeros of Bargmann functions. Hadamard's theorem is expressed in a physical language and it is used to construct quantum states, with given zeros in their Bargmann function. Various examples are discussed. The time evolution of Bargmann functions and the motion of their zeros, for various Hamiltonians, is studied.
The growth of Bargmann functions is intimately connected to the density of the zeros of these functions and to the completeness of sequences of coherent states. Using these ideas we find the least density that a sequence of coherent states must have in order to be overcomplete within the space of Bargmann functions of an order not exceeding (and of a type not exceeding if of order ). These results generalize known results on the completeness of von Neumann lattices. The practical significance of this formalism in the context of quantum optics is also discussed.
The paper contains an investigation of zeros Of Bargmann analytic representation. A brief introduction to Harmonic oscillator formalism is given. The Bargmann analytic representation has been studied. The zeros of Bargmann analytic function are considered. The Q or Husimi functions are introduced. The The Bargmann functions and the Husimi functions have the same zeros. The Bargmann functions f(z) have exactly q zeros. The evolution time of the zeros μn are discussed. Various examples have been given.