Weight Construction in Extended Space Expectation Values for Singular Quantum Systems at Spectral Structuring and Temporal Constancy Limit

Abstract

We have recently shown that the operator expectation values for the quantum dynamical systems of singular Hamiltonians, cannot be expanded into temporal Maclaurin series. Depending on the nature of the system under consideration and the relevant operator, either a finite number of terms can exist while the others become infinite or the series can convergence only at the beginning of the evolution even if the coefficients of the series all exist. This however happens when the initial wave packet has some features leading us to nonintegrabilities in certain expectation values. The reason why this happens underlies beneath the fact that the certain images of the initial wave packet under certain natural number powers of the Hamiltonian become nonintegrable. This negativity can be bypassed by using certain weight functions in the expectation value definition and corresponds to working on an extended space constructed from the Hilbert space in which the initial and any time wave function lay. We have used a two parameter weight function in our most recent publication. Here, in this work, we extend the weight function to multiparameter structures where the number of parameters is more than two and may climb even up to infinity.