Series expansion of a function's expectation matrix at the zero interval length limit

Demiralp M.

International Conference on Numerical Analysis and Applied Mathematics, Corfu, Greece, 16 - 20 September 2007, vol.936, pp.155-158 identifier

  • Publication Type: Conference Paper / Full Text
  • Volume: 936
  • City: Corfu
  • Country: Greece
  • Page Numbers: pp.155-158
  • Istanbul Technical University Affiliated: No


Expectation matrix of a function serves us to evaluate the expectation value of an algebraic multiplication-by-a-function type operator over a specified subspace of a given Hilbert space. It is also frequently called transition matrix due to quantum mechanical tradition. This work considers univariate functions on finite intervals. The elements of expectation matrix of such a given function are univariate integrals which can be expanded into powers of the interval length and the resulting series may converge in a disc with a certain radius located at the expansion point in the independent variable's complex plane. Convergence and practical applicability issues are also given.