Univariate Single Quantum Harmonic Oscillator from Probabilistic Evolution Perspective

摘要

This work considers the application of the recently developed "Probabilistic Evolution Approach" to the quantum dynamical systems. The purpose is to show that the only difference from the ODEs case is the difference in the initial conditions as long as the expectation values dynamics is considered. For illustrative purposes, the single quantum harmonic oscillator is taken into consideration. The triangularity and first order recursive nature appearing in the evolution matrix facilitates the analysis very much in many cases. Far beyond this facilitation, this very particular system has much simpler structure by having block diagonal evolution matrix but gives all desired clues about the probabilistic evolution's true probabilistic nature.