7 research outputs found
The Time-Energy Uncertainty Relation
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.Comment: 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 literatur
Strong time operators associated with generalized Hamiltonians
Let the pair of operators, , satisfy the weak Weyl relation:
, where is self-adjoint and is closed
symmetric. Suppose that g is a realvalued Lebesgue measurable function on \RR
such that for some closed subset K \subset \RR with Lebesgue
measure zero. Then we can construct a closed symmetric operator such that
also obeys the weak Weyl relation.Comment: 10 page