A New Look at the Position Operator in Quantum Theory

An operator calculus is developed applicable to problems in the electron theory of metals. It differs from the common operator calculus of the quantum theory in the fact that the wave function is defined in a finite space (the atomic polyhedron) bounded by a finite surface. This leads to the introduction of surface operators. The position operator x cannot be developed with respect to the proper functions of the Hamiltonian. Instead an operator ξ is introduced, which is essentially the Fourier development of x. Thus there are three fundamental types of operators: the differential operator p, the multiplication operator ξ and the surface operators. It is shown that with the help of these a consistent calculus can be developed.

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QUEST FOR THE TIME OPERATOR WITH A SINGLE TRAPPED ION

International Journal of Quantum Information ◽

10.1142/s0219749911007307 ◽

2011 ◽

Vol 09 (supp01) ◽

pp. 189-202 ◽

Cited By ~ 3

Author(s):

CAROLINE CHAMPENOIS ◽

THOMAS DURT

Keyword(s):

Quantum Theory ◽

Time Operator ◽

Position Operator ◽

Experimental Physics ◽

Trapped Ion ◽

Quantum Time ◽

Decay Times ◽

The Status ◽

Open Question ◽

Crucial Experiments

The status of Time in the Quantum Theory remains even today a largely open question. In particular, the existence of a Quantum Time Operator that would describe the distribution of decay times of an unstable quantum system (in analogy with the Position operator that is associated to the position distribution) remained a polemichal question during several decades. Recently, we conceived experimental proposals involving CP violating processes (of single mesons and entangled pairs of mesons) that can be considered as crucial experiments aimed at testing the existence of a Quantum Time Operator. In the present paper, we shall present a similar proposal that can be realized with a single trapped ion. These proposals aim at bringing fundamental problems related to the status of Time in the Quantum Theory to the realm of experimental physics.

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