Phase Space Picture of Quantum Mechanics

Kim, Y S; Noz, Marilyn E.

doi:10.1142/1197

Cited by 201 publications

(236 citation statements)

References 0 publications

Supporting

Mentioning

233

Contrasting

Unclassified

Order By: Relevance

“…This is the fundamental two-dimensional representation of the SL(2, C) ∼ Sp(2, C)-group which in case of unitary squeezing operators [42,43]. The matrices of this representation in (3.7) are complex unimodular or symplectic but in general not unitary.…”

Section: Transformation Properties Of the Radon Transform Of The Wignmentioning

confidence: 99%

Radon transform and pattern functions in quantum tomography

Wünsche¹

1997

Journal of Modern Optics

View full text Add to dashboard Cite

The two-dimensional Radon transform of the Wigner quasiprobability is introduced in canonical form and the functions playing a role in its inversion are discussed. The transformation properties of this Radon transform with respect to displacement and squeezing of states are studied and it is shown that the last is equivalent to a symplectic transformation of the variables of the Radon transform with the contragredient matrix to the transformation of the variables in the Wigner quasiprobability. The reconstruction of the density operator from the Radon transform and the direct reconstruction of its Fock-state matrix elements and of its normally ordered moments are discussed. It is found that for finite-order moments the integration over the angle can be reduced to a finite sum over a discrete set of angles. The reconstruction of the Fock-state matrix elements from the normally ordered moments leads to a new representation of the pattern functions by convergent series over even or odd Hermite polynomials which is appropriate for practical calculations. The structure of the pattern functions as first derivatives of the products of normalizable and nonnormalizable eigenfunctions to the number operator is considered from the point of view of this new representation.

show abstract

Section: Transformation Properties Of the Radon Transform Of The Wignmentioning

confidence: 99%

Radon transform and pattern functions in quantum tomography

Wünsche¹

1997

Journal of Modern Optics

View full text Add to dashboard Cite

show abstract

“…He then ends up with ten operators which act like the generators of of the O(3, 2) deSitter group. In so doing he constructed the scientific language of two-photon coherent states or squeezed states of light which became an important branch of physics 20 years later [7]. The O(3, 1) Lorentz group is a subgroup of O (3, 2).…”

Section: Dirac's Coupled Oscillatorsmentioning

confidence: 99%

“…In 1963 [6], Dirac used two coupled oscillators to construct a representation of the O(3, 2) deSitter group which later became the basic mathematical base for two-photon coherent states known as squeezed states of light [7].…”

Section: Introductionmentioning

confidence: 99%

Can you do quantum mechanics without Einstein?

Kim¹,

Noz²

2007

AIP Conference Proceedings

View full text Add to dashboard Cite

The present form of quantum mechanics is based on the Copenhagen school of interpretation. Einstein did not belong to the Copenhagen school, because he did not believe in probabilistic interpretation of fundamental physical laws. This is the reason why we are still debating whether there is a more deterministic theory. One cause of this separation between Einstein and the Copenhagen school could have been that the Copenhagen physicists thoroughly ignored Einstein's main concern: the principle of relativity. Paul A. M. Dirac was the first one to realize this problem. Indeed, from 1927 to 1963, Paul A. M. Dirac published at least four papers to study the problem of making the uncertainty relation consistent with Einstein's Lorentz covariance. It is interesting to combine those papers by Dirac to make the uncertainty relation consistent with relativity. It is shown that the mathematics of two coupled oscillators enables us to carry out this job. We are then led to the question of whether the concept of localized probability distribution is consistent with Lorentz covariance.

show abstract

“…In this framework the coordinates and momenta are considered simultaneously, which gives a natural extension of the Hamiltonian construction to describe quantum systems. A complete review of this topic can be found in [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

“…The Wigner function has been employed widely in quantum optics, condensed matter, nuclear and particle physics, etc. A comprehensive guide to these applications can be found in [7] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%