On the problem of time in quantum mechanics. (1st March 2017)

• Record Type: Journal Article
• Authors: Bauer, M
• Is Part Of: European journal of physics. Volume 38:Number 3(2017:May)
• Publication Date: 2017-03-01
• Subjects: time operator -- relativistic quantum mechanics -- time–energy uncertainty relation; 03.65.-w -- 03.65.Ca -- 03.65.Pm; Physics -- Periodicals; Physics -- Study and teaching (Higher) -- Europe -- Periodicals; 530
• DOI: 10.1088/1361-6404/aa6025
• Languages: English
• ISSNs: 0143-0807

Abstract

Abstract: The problem of time in quantum mechanics (QM) concerns the fact that in the Schrödinger equation time is a parameter, not an operator. Pauli's objection to a time–energy uncertainty relation analogue to the position–momentum one, conjectured by Heisenberg early on, seemed to exclude the existence of such an operator. However Dirac's formulation of an electron's relativistic QM does allow the introduction of a dynamical time operator that is self-adjoint. Consequently, it can be considered as the generator of a unitary transformation of the system, as well as an additional system observable subject to uncertainty. In the present paper these aspects are examined within the standard framework of relativistic QM.