Time-evolution of an observer means how it changes over time; it's derivative over time. In quantum mechanics, it is described by the Hamiltonian. DO NOT use this tag for evolving laws of physics.

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Time Evolution Operator in Interaction Picture (Harmonic Oscillator with Time Dependent Perturbation)

1. The problem statement, all variables and given/known data Consider a time-dependent harmonic oscillator with Hamiltonian $$\hat{H}(t)=\hat{H}_0+\hat{V}(t)$$ $$\hat{H}_0=\hbar \omega \left( ...