Wavefunctions on phase space

Smith, Thomas

doi:10.1088/0305-4470/39/6/019

Cited by 14 publications

(19 citation statements)

References 22 publications

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“…The wave functions ψ σ (p, q) were defined in reference [18] where many of their properties are discussed. In particular, they are the Weyl transform of the operators |ψ σ|.…”

Section: Wave Functions On Phase Spacementioning

confidence: 99%

“…The generalization of ψ σ (p, q) to the family of orderings defined by equations (14) and (15) is given [18] by…”

Section: Wave Functions On Phase Spacementioning

confidence: 99%

“…A given value of λ specifies an association between functions on phase space and operators, A(p, q) (λ) ←→Â, where λ = −1 gives the standard ordering (eg p n q m ←→ q mp n ), λ = +1 gives the anti-standard rule (eg p n q m ←→p nq m ), and λ = 0 gives the symmetric or Weyl association, of which (1) σ (p, q) itself, has been studied in [18]. ψ…”

Section: Introductionmentioning

confidence: 99%

“…The time-dependence of Q σ (p, q) itself which enters through the time-dependence of |ψ . In [18] it was chosen to study the time variation of ψ …”

mentioning

confidence: 99%

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GeneralizedQ-functions

Smith¹

2006

J. Phys. A: Math. Gen.

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The modulus squared of a class of wave functions defined on phase space is used to define a generalized family of Q or Husimi functions. A parameter λ specifies orderings in a mapping from the operator |ψ σ| to the corresponding phase space wave function, where σ is a given fiducial vector. The choice λ = 0 specifies the Weyl mapping and the Q-function so obtained is the usual one when |σ is the vacuum state. More generally, any choice of λ in the range (−1, 1) corresponds to orderings varying between standard and anti-standard. For all such orderings the generalized Q-functions are non-negative by construction. They are shown to be proportional to the expectation of the system stateρ with respect to a generalized displaced squeezed state which depends on λ and position (p, q) in phase space. Thus, when a system has been prepared in the stateρ, a generalized Q-function is proportional to the probability of finding it in the generalized squeezed state. Any such Q-function can also be written as the smoothing of the Wigner function for the system stateρ by convolution with the Wigner function for the generalized squeezed state.

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“…The wave functions ψ σ (p, q) were defined in reference [18] where many of their properties are discussed. In particular, they are the Weyl transform of the operators |ψ σ|.…”

Section: Wave Functions On Phase Spacementioning

confidence: 99%

“…The generalization of ψ σ (p, q) to the family of orderings defined by equations (14) and (15) is given [18] by…”

Section: Wave Functions On Phase Spacementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…The time-dependence of Q σ (p, q) itself which enters through the time-dependence of |ψ . In [18] it was chosen to study the time variation of ψ …”

mentioning

confidence: 99%

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GeneralizedQ-functions

Smith¹

2006

J. Phys. A: Math. Gen.

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“…then (20) becomes the spin Husimi function [32]. The product of two spherical harmonics with the same arguments can be written as a linear combination of single spherical harmonics in terms of the 3j -symbols; hence (19) can be reexpressed as…”

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confidence: 99%

Phase-space spinor amplitudes for spin-1/2systems

Watson

Bracken

2011

Phys. Rev. A

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The concept of phase-space amplitudes for systems with continuous degrees of freedom is generalized to finite-dimensional spin systems. Complex amplitudes are obtained on both a sphere and a finite lattice, in each case enabling a more fundamental description of pure spin states than that previously given by Wigner functions. In each case the Wigner function can be expressed as the star product of the amplitude and its conjugate, so providing a generalized Born interpretation of amplitudes that emphasizes their more fundamental status. The ordinary product of the amplitude and its conjugate produces a (generalized) spin Husimi function. The case of spin -1 2 is treated in detail, and it is shown that phase-space amplitudes on the sphere transform correctly as spinors under rotations, despite their expression in terms of spherical harmonics. Spin amplitudes on a lattice are also found to transform as spinors. Applications are given to the phase space description of state superposition, and to the evolution in phase space of the state of a spin-1 2 magnetic dipole in a time-dependent magnetic field.

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Deformation Theory of Classical Poisson Algebras

Błaszak¹

2019

Quantum Versus Classical Mechanics and Integrability Problems

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Wavefunctions on phase space

Cited by 14 publications

References 22 publications

GeneralizedQ-functions

GeneralizedQ-functions

Phase-space spinor amplitudes for spin-1/2systems

Deformation Theory of Classical Poisson Algebras

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