A position operator for the photon. Giving up the complementarity principle

The article deals with the problem of the epistemological status of the complementarity principle in socio-humanitarian studies. It clarifies the content of the principle of complementarity and the possibility of its application from the point of view of its methodological significance for studying the interdependence of language, world view and the picture of the world. It is shown that the authentic application of the principle is possible within the framework of a constructionist epistemological model, subject to a number of methodological requirements for the organization of the research process. To correlate the complementary description languages in the designated problem area, the interdisciplinary conceptual apparatus of cultural studies seems productive.

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The four-dimensional position operator in theories with broken conformal symmetry

Il Nuovo Cimento A ◽

10.1007/bf02730001 ◽

1976 ◽

Vol 32 (2) ◽

pp. 174-184 ◽

Cited By ~ 4

Author(s):

Z. Haba

Keyword(s):

Conformal Symmetry ◽

Position Operator

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q-Equivalent Hamiltonian Operators

Canadian Journal of Physics ◽

10.1139/p72-271 ◽

1972 ◽

Vol 50 (17) ◽

pp. 2037-2047 ◽

Cited By ~ 16

Author(s):

M. Razavy

Keyword(s):

Quantum Mechanics ◽

Classical Limit ◽

First Integral ◽

Canonical Commutation Relation ◽

Equation Of Motion ◽

First Integrals ◽

Position Operator ◽

Integrals Of Motion ◽

Adjoint Operators ◽

Hamiltonian Operators

From the equation of motion and the canonical commutation relation for the position of a particle and its conjugate momentum, different first integrals of motion can be constructed. In addition to the proper Hamiltonian, there are other operators that can be considered as the generators of motion for the position operator (q-equivalent Hamiltonians). All of these operators have the same classical limit for the probability density of the coordinate of the particle, and many of them are symmetric and self-adjoint operators or have self-adjoint extensions. However, they do not satisfy the Heisenberg rule of quantization, and lead to incorrect commutation relations for velocity and position operators. Therefore, it is concluded that the energy first integral and the potential, rather than the equation of motion and the force law, are the physically significant operators in quantum mechanics.

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