2010/11/23 by Yoshihiro Sato, Arno Böhm, Sato, Yoshihiro +1
Computer Science · Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mathematical Physics (math-ph) #Mechanical and Optical Resonators #Nonlinear Dynamics and Pattern Formation #Quantum Mechanics and Applications #Quantum Physics (quant-ph)
paper · pdf · doi:10.48550/arxiv.1011.5195
openalex publication_date 2010/11/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In quantum physics, disturbance due to a measurement is not negligible. This\nrequires the time parameter t in the Schr "odinger or Heisenberg equation to\nbe considered differently from a time continuum of experimenter's clock T on\nwhich physical events are recorded. It will be shown that t represents an\nensemble of time intervals on T during which a microsystem travels\nundisturbed. In particular t=0 represents the ensemble of preparation events\nthat we refer to as the ensemble of beginnings of time. This restricts t to\nbe 0\≤ t<\∞. But such a time evolution of quantum states cannot be\nachieved in the Hilbert space L2 functions because due to the Stone-von\nNeumann theorem this time evolution is given by the unitary group with t\nextending -\∞<t<\∞. Hence one needs solutions of the Schr "odinger\n(and Heisenberg) equation under time asymmetric boundary condition in which\nonly the semigroup time evolution is allowed. This boundary condition is\nfulfilled by the energy wave functions for quantum states (and as well as for\nobservables) which are smooth Hardy function satisfying the Hilbert transform,\ncalled the dispersion relation in physics.\n