HOLOMORPHIC FUNCTIONAL CALCULUS APPROACH TO THE CHARACTERISTIC FUNCTION OF QUANTUM OBSERVABLES
HOLOMORPHIC FUNCTIONAL CALCULUS APPROACH TO THE CHARACTERISTIC FUNCTION OF QUANTUM OBSERVABLES
We show how Cauchy’s Integral Formula and the ideas of Dunford’s Holomorphic Functional Calculus (for unbounded operators) can be used to compute the Vacuum Characteristic Function (Quantum Fourier Transform) of quantum random variables defined as self-adjoint operators on L2(R,C). We consider in detail several quantum observables defined in terms of …