Abstract
The role of time in quantum mechanics has been and is still very controversial. The purpose of this paper was to explore the historical interpretation of time in quantum mechanics, to determine the current status of this problem-L and to investigate the possibility of having a derived duration time operator in the micromaser. In the past, time has been treated as a discrete quantity, as an operator, and as a derived quantity. Recently, Scully found that time was a derived quantity in the micromaser. Scully then suggested that this time was an operator. Upon investigation, it was found that this time operator [ ] could be interpreted as an integral operator. Sussmann found that a representation of the inverse momentum operator existed such that [pp=1=pp]. Further investigation of the commutator relation revealed that [x] and [ ] are incompatible. However, they could not be paired as conjugate variables because their commutator relation is not equal to an unit of action. The Pauli objection is found to be inapplicable in this problem because [H-system] and [ ] were found to commute. Pauli's objection was based on the fact that the commutator relation of [H-system] and [ ] was equal to an unit of action. Finally, interpreting [ ] as a time of motion, the analog of the lifetime matrix for the micromaser was calculated. It was found to represent the projection of a rotation (i.e. a phase shift).
Chapin, Kimberly R. (1997). Time in quantum mechanics. Master's thesis, Texas A&M University. Available electronically from
https : / /hdl .handle .net /1969 .1 /ETD -TAMU -1997 -THESIS -C4425.