Spectral Theorem Approach to the Characteristic Function of Quantum Observables
Andreas Boukas, Philip Feinsilver · Civil War Book Review · 2019
Using the spectral theorem we compute the Quantum Fourier Transform or Vacuum Characteristic Function Φ, e itH Φ of an observable H defined as a self-adjoint sum of the generators of a finite-dimensional Lie algebra, where Φ is a unit vector in a Hilbert space H.We show how Stone's formula for computing the spectral resolution of a Hilbert space self-adjoint operator, can serve as an alternative to the traditional reliance on splitting or disentanglement formulas for the operator exponential.