Abstract: 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.
Abstract: The paper contains an investigation of winding numbers
of paths of zeros of analytic theta functions. We have considered
briefly an analytic representation of finite quantum systems ZN.
The analytic functions on a torus have exactly N zeros. The brief
introduction to the zeros of analytic functions and there time evolution
is given. We have discussed the periodic finite quantum systems. We
have introduced the winding numbers in general. We consider the
winding numbers of the zeros of analytic theta functions.
Abstract: The paper contains an investigation on basic problems
about the zeros of analytic theta functions. A brief introduction to
analytic representation of finite quantum systems is given. The zeros
of this function and there evolution time are discussed. Two open
problems are introduced. The first problem discusses the cases when
the zeros follow the same path. As the basis change the quantum state
|f transforms into different quantum state. The second problem is
to define a map between two toruses where the domain and the range
of this map are the analytic functions on toruses.