aqora

Phase space quantization and the uncertainty principle

Maurice A. de Gosson

Physics Letters ASep 22, 200343 citations

On the quantization of classical systems

J.-P. Amiet

Il Nuovo CimentoJul 1, 19634 citations

Schrodinger equation from an exact uncertainty principle

Hall, M J W, Reginatto, M

An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position, leads from the classical equations of motion to the Schrodinger equation. Thus there is an exact formulation of the uncertainty principle which precisely captures the essence of what is "quantum" about quantum mechanics.

Feb 13, 200181 citations

Schrödinger equation from an exact uncertainty principle

Michael J. W. Hall, Marcel Reginatto

An exact uncertainty principle, formulated as the assumption that a classical ensemble is subject to random momentum fluctuations of a strength which is determined by and scales inversely with uncertainty in position, leads from the classical equations of motion to the Schrödinger equation.

arXiv:quant-ph/0102069Journal of Physics A Mathematical and GeneralMar 28, 2002108 citations

The quantization of classical systems

P. B. Guest

Reports on Mathematical PhysicsSep 1, 19744 citations

Bosonic field equations from an exact uncertainty principle

Michael J. W. Hall, K. Vijay Kumar, Marcel Reginatto

A Hamiltonian formalism is used to describe ensembles of fields in terms of two canonically conjugate functionals (one being the field probability density). The postulate that a classical ensemble is subject to nonclassical fluctuations of the field momentum density, of a strength determined solely by the field uncertainty, is shown to lead to a unique modification of the ensemble Hamiltonian. The modified equations of motion are equivalent to the quantum equations for a bosonic field, and thus this exact uncertainty principle provides a new approach to deriving and interpreting the properties of quantum ensembles. The examples of electromagnetic and gravitational fields are discussed. In the latter case, the exact uncertainty approach specifies a unique operator ordering for the Wheeler–DeWitt and Ashtekar–Wheeler–DeWitt equations.A Hamiltonian formalism is used to describe ensembles of fields in terms of two canonically conjugate functionals (one being the field probability density). The postulate that a classical ensemble is subject to nonclassical fluctuations of the field momentum density, of a strength determined solely by the field uncertainty, is shown to lead to a unique modification of the ensemble Hamiltonian. The modified equations of motion are equivalent to the quantum equations for a bosonic field, and thus this exact uncertainty principle provides a new approach to deriving and interpreting the properties of quantum ensembles. The examples of electromagnetic and gravitational fields are discussed. In the latter case, the exact uncertainty approach specifies a unique operator ordering for the Wheeler–DeWitt and Ashtekar–Wheeler–DeWitt equations.

arXiv:hep-th/0307259Journal of Physics A Mathematical and GeneralSep 2, 200336 citations

Quantization of Classical Ensembles via an Exact Uncertainty Principle

Related papers

Quantization of Classical Ensembles via an Exact Uncertainty Principle

Related papers