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Comment on "TIME OPERATOR": THE CHALLENGE PERSISTS

Jerzy Kijowski, Centrum Fizyki, Teoretycznej Pan

Published Jan 1, 2005• 0 citations
OpenAlex

Abstract

The criticism formulated by Mielnik and Torres-Vega in their paper, does not apply to my derivation of the time of arrival in Quantum Mechanics but to our present understanding of the quantum measurement theory.

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Contrary to claims contained in papers by Grot, Rovelli, and Tate [Phys. Rev. A 54, 4676 1996)] and Delgado and Muga [Phys. Rev. A 56, 3425 (1997)], the ``time operator,'' which I have constructed [Rep. Math. Phys. 6, 361 (1974)] in an axiomatic way, is a self-adjoint operator existing in a usual Hilbert space of (nonrelativistic or relativistic) quantum mechanics.

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Wavefunctions on phase space

T B Smith

Theories of Torres-Vega and Fredrick (1993 J. Chem. Phys. 98 3103), Harriman (1994 J. Chem. Phys. 100 3651) and of Ban (1998 J. Math. Phys. 39 1744), in which phase space points ( p , q ) are used as configurational variables to formulate quantum mechanics are considered from the standpoint of a class of quantization schemes associating phase space functions with operators. The connection between these schemes and the theories given in Torres-Vega and Fredrick (1993 J. Chem. Phys. 98 3103), Harriman (1994 J. Chem. Phys. 100 3651), Dirac (1930 The Principles of Quantum Mechanics (Oxford: Oxford University Press)), Møller, Jørgensen and Torres-Vega (1997 J. Chem. Phys. 106 7228), Klauder and Skagerstam (1985 Coherent States: Applications in Physics and Mathematical Physics (Singapore: World Scientific)), Li, Wei and Lü (2004 Phys. Rev. A 70 022105), Ban (1998 J. Math. Phys. 39 1744) is made by means of augmented wavefunctions ψ (λ) σ ( p , q ; t ), where λ = 0 corresponds to the ordering of Wigner and Weyl. For that case we use these functions to define a family of positive operator-valued measures for the phase angle of an harmonic oscillator.

Journal of Physics A Mathematical and General•Jan 24, 2006•12 citations

"Time operator": the challenge persists

Bogdan Mielnik, Gabino Torres-Vega

Contrary to the conviction expressed by J. Kijowski [Phys. Rev. A 59, 897 (1999)] and shared in some other papers, the reasons to look for the 'time operator' in the context of the standard quantum doctrine of orthogonal projectors and self-adjoint observables are highly questionable. Some improved solutions in terms of POV measures invite critical discussions as well.

arXiv:1112.4198•Dec 18, 2011•12 citations
Theories of Torres-Vega and Fredrick (1993 J. Chem. Phys. 98 3103), Harriman (1994 J. Chem. Phys. 100 3651) and of Ban (1998 J. Math. Phys. 39 1744), in which phase space points ( p , q ) are used as configurational variables to formulate quantum mechanics are considered from the standpoint of a class of quantization schemes associating phase space functions with operators. The connection between these schemes and the theories given in Torres-Vega and Fredrick (1993 J. Chem. Phys. 98 3103), Harriman (1994 J. Chem. Phys. 100 3651), Dirac (1930 The Principles of Quantum Mechanics (Oxford: Oxford University Press)), Møller, Jørgensen and Torres-Vega (1997 J. Chem. Phys. 106 7228), Klauder and Skagerstam (1985 Coherent States: Applications in Physics and Mathematical Physics (Singapore: World Scientific)), Li, Wei and Lü (2004 Phys. Rev. A 70 022105), Ban (1998 J. Math. Phys. 39 1744) is made by means of augmented wavefunctions ψ (λ) σ ( p , q ; t ), where λ = 0 corresponds to the ordering of Wigner and Weyl. For that case we use these functions to define a family of positive operator-valued measures for the phase angle of an harmonic oscillator.