The Time-Energy Uncertainty Relation
arXiv:quant-ph/0105049 · doi:10.1007/978-3-540-73473-4_3
Abstract
The time energy uncertainty relation has been a controversial issue since the advent of quantum theory, with respect to appropriate formalisation, validity and possible meanings. A comprehensive account of the development of this subject up to the 1980s is provided by a combination of the reviews of Jammer (1974), Bauer and Mello (1978), and Busch (1990). More recent reviews are concerned with different specific aspects of the subject. The purpose of this chapter is to show that different types of time energy uncertainty relation can indeed be deduced in specific contexts, but that there is no unique universal relation that could stand on equal footing with the position-momentum uncertainty relation. To this end, we will survey the various formulations of a time energy uncertainty relation, with a brief assessment of their validity, and along the way we will indicate some new developments that emerged since the 1990s.
33 pages, Latex. This expanded version (prepared for the 2nd edition of "Time in quantum mechanics") contains minor corrections, new examples and pointers to some additional relevant literature
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- Understanding quantum mechanics: a review and synthesis in precise language
- Classical and Nonclassical Time Dilation for Quantum Clocks
- Classical mechanics in reparametrization-invariant formulation and the Schrödinger equation
- Timelessness strictly inside the Quantum Realm
- Uncertainty relations for time averaged weak values
- Characteristic time operators as quantum clocks
- Uncertainty principle, Shannon-Nyquist sampling and beyond
- Empirical adequacy of the time operator canonically conjugate to a Hamiltonian generating translations
- Higher-order uncertainty bounds for mixed states
- Quantum arrival times in free fall