From the Quantum Harmonic Oscillator to the Orstein-Uhlenbeck Process and Back

In this thesis, the relation between the generator of the OrnsteinUhlenbeck process and the Hamiltonian of the quantum harmonic oscillator is used to derive a new understanding of the evolution of certain quantum states. More precisely, we transform the Hamiltonian with respect to the ground state and corresponding eigenvalue to find that it is...