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, Yunanistan, 16 - 20 Eylül 2007, cilt.936, ss.155-158 identifier

  • Cilt numarası: 936
  • Basıldığı Şehir: Corfu
  • Basıldığı Ülke: Yunanistan
  • Sayfa Sayıları: ss.155-158


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.