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Time as an observable in nonrelativistic quantum mechanics

2003
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Journal of Physics A: Mathematical and General
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The nonrelativistic Schroedinger equation for motion of a structureless particle in four-dimensional space-time entails a well-known expression for the conserved four-vector field of local probability density and current that are associated with a quantum state solution to the equation. Under the physical assumption that each spatial, as well as the temporal, component of this current is observable, the position in time becomes an operator and an observable in that the weighted average value of

doi:10.1088/0305-4470/36/25/316
fatcat:tuvl4jsq2veqxirazluam26jcm