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• W2075606972 endingPage "2134" @default.
• W2075606972 startingPage "2126" @default.
• W2075606972 abstract "A previously developed novel theory for the formal canonical quantization of classically dissipating systems will be the starting point for a detailed discussion of the quantum statistical aspects of the simple linearly damped harmonic oscillator. The formalism essentially involves complex classical canonical coordinates and momenta, and thus quite naturally leads to the possibility of creation and annihilation operators. Furthermore, the occurrence of quantal noise operators appears to be of principal importance for the conservation of the fundamental commutator in the course of time, as will be expressed in a simple fluctuation-dissipation relation. Making a canonical transformation back to the real, Cartesian Hermitian position and momentum an effective Hermitian Hamiltonian will be derived, with which a transformation is made from the Heisenberg frame to the Schrodinger frame where the density operator equation will be computed. This will make it obvious that no proper Schrodinger equation exists for the dissipative subsystem on its own, thus reflecting an incomplete knowledge. The master equation will then be translated into its Wigner representation. The intimate connection between the diffusion coefficients in the resulting Fokker-Planck equation and the uncertainty relation will be demonstrated in a clear fashion." @default.
• W2075606972 created "2016-06-24" @default.
• W2075606972 creator A5061035231 @default.
• W2075606972 date "1977-11-01" @default.
• W2075606972 modified "2023-09-24" @default.
• W2075606972 title "Quantization of the linearly damped harmonic oscillator" @default.
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• W2075606972 doi "https://doi.org/10.1103/physreva.16.2126" @default.
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