2007/01/13 by S. Teerenstra, Teerenstra, S.
Physics and Astronomy · #FOS: Physical sciences #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.quant-ph/0701082
openalex publication_date 2007/01/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Quantization of the damped harmonic oscillator is taken as leitmotiv to gently introduce elements of quantum probability theory for physicists. To this end, we take (graduate) students in physics as entry level and explain the physical intuition and motivation behind the, sometimes overwhelming, math machinery of quantum probability theory. The main text starts with the quantization of the (undamped) harmonic oscillator from the Heisenberg and Schroedinger point of view. We show how both treatments are special instances of a quantum probabilistic quantization procedure: the second quantization functor. We then apply the second quantization functor to the damped harmonic oscillator and interpret the quantum dynamics of the position and energy operator as stochastic processes.