1999/05/11 by Jan Myrheim, Myrheim, Jan · 1 voice · 12 citations
Chemistry · Mathematics · Physics and Astronomy · #Algorithm #Canonical quantization #Classical mechanics #Eigenvalues and eigenvectors #FOS: Physical sciences #Generalization #Harmonic oscillator #High Energy Physics - Theory (hep-th) #Hilbert space #Mathematical analysis #Mathematical formulation of quantum mechanics #Mathematics #Molecular spectroscopy and chirality #Observable #Operator (biology) #POVM #Physics #Pure mathematics #Quantization (signal processing) #Quantum #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Quantum dynamics #Quantum gravity #Quantum mechanics #Quantum optics and atomic interactions #Quantum process #Quantum statistical mechanics #Reproducing kernel Hilbert space #Rigged Hilbert space #SIC-POVM #Supersymmetric quantum mechanics #Theoretical physics #hep-th #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9905037
published in arXiv (Cornell University) (Cornell University) · 13 pages, LaTeX, no figures
arxiv created 1999/05/11 · openalex publication_date 1999/05/11 · arxiv published 1999/05/11 · arxiv updated 1999/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
The complex Hilbert space of standard quantum mechanics may be treated as a real Hilbert space. The pure states of the complex theory become mixed states in the real formulation. It is then possible to generalize standard quantum mechanics, keeping the same set of physical states, but admitting more general observables. The standard time reversal operator involves complex conjugation, in this sense it goes beyond the complex theory and may serve as an example to motivate the generalization. Another example is unconventional canonical quantization such that the harmonic oscillator of angular frequency ω has any given finite or infinite set of discrete energy eigenvalues, limited below by ℏω/2.