The problem of time in quantum mechanics

Abstract

The problem of time in quantum mechanics 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 electron's relativistic quantum mechanics (RQM) 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 RQM.

References in corpus (3)

• Unified description of the Zitterbewegung for spintronic, graphene and superconducting systems
• Time as a quantum observable
• The time as an emergent property of quantum mechanics, a synthetic description of a first experimental approach

Cited by in corpus (5)

• Tunneling in attosecond optical ionization and a dynamical time operator
• Challenging $\Lambda$CDM with Higher-Order GUP Corrections
• Linear Canonical Transformations in Relativistic Quantum Physics
• Time and energy operators in the canonical quantization of special relativity
• Thermodynamic origin of quantum time-energy uncertainty relation