Variance of the quantum dwell time for a nonrelativistic particleG. E. Hahne
- Journal of Mathematical Physics, January 2013, American Institute of Physics
- DOI: 10.1063/1.4776657
Time t as an operator in quantum mechanics: variance, etc.
What is it about?
I have claimed that, contrary to the 80-year-old CW, the "parameter" t is the correct operator for time in NRQM. Its operator properties are manifested in spacewise, as contrasted with the usual timewise, evolution of wave functions. This paper elaborates by deriving analogs to the formulas for variance, and for measurement compatibilities with other physical quantities, of the total time t that a particle spends in a spatially limited, but possibly temporally unlimited, region.
Why is it important?
A substantial body of published research has claimed that the that the problem of finding an operator tor time in QM is as yet incompletely solved, with numerous, often complex, proposals for possible resolutions having been made. I maintain that the concept is easy, and in this paper obtain formulas that admit of prediction, experimental verification, and possible applications to (say) condensed-matter physics.