Almost-periodic time observables for bound quantum systems

Details Almost-periodic time observables for bound quantum systems Almost-periodic time observables for bound quantum systems

2008-03-26

arxiv.org/abs/0803.3721v3

J. Phys. A 41 (2008) 255301

Physics

Quantum Physics

v2: Bound for 'typical' entropy corrected (no more than 1 bit of 'time' information in a bound hydrogen atom) v3: minor clarif

Scientific paper

10.1088/1751-8113/41/25/255301

It is shown that a canonical time observable may be defined for any quantum system having a discrete set of energy eigenvalues, thus significantly generalising the known case of time observables for periodic quantum systems (such as the harmonic oscillator). The general case requires the introduction of almost-periodic probability operator measures (POMs), which allow the expectation value of any almost-periodic function to be calculated. An entropic uncertainty relation for energy and time is obtained which generalises the known uncertainty relation for periodic quantum systems. While non-periodic quantum systems with discrete energy spectra, such as hydrogen atoms, typically make poor clocks that yield no more than 1 bit of time information, the anisotropic oscillator provides an interesting exception. More generally, a canonically conjugate observable may be defined for any Hermitian operator having a discrete spectrum.

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