An interesting property of the Husimi function and its implications

Davidović, Dragomir; Lalović, Dragutin; Tančić, A.R.

doi:10.1088/0305-4470/27/24/029

Cited by 6 publications

(6 citation statements)

References 4 publications

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“…It was shown in [29] that if λ 2 ≤ 1 and Q(q, p) is a Husimi function, then Q λ (q, p) is also a Husimi function of some physical state. We give a new proof of this in the appendix.…”

Section: Transformations Of the Husimi And Wigner Functionsmentioning

confidence: 99%

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A transformational property of the Husimi function and its relation to the wigner function and symplectic tomograms

Andreev

Davidović

et al. 2011

Theor Math Phys

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We consider the Husimi Q-functions, which are quantum quasiprobability distributions in the phase space, and investigate their transformation properties under a scale transformation (q, p) → (λq, λp). We prove a theorem that under this transformation, the Husimi function of a physical state is transformed into a function that is also a Husimi function of some physical state. Therefore, the scale transformation defines a positive map of density operators. We investigate the relation of Husimi functions to Wigner functions and symplectic tomograms and establish how they transform under the scale transformation. As an example, we consider the harmonic oscillator and show how its states transform under the scale transformation.

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“…It was shown in [29] that if λ 2 ≤ 1 and Q(q, p) is a Husimi function, then Q λ (q, p) is also a Husimi function of some physical state. We give a new proof of this in the appendix.…”

Section: Transformations Of the Husimi And Wigner Functionsmentioning

confidence: 99%

“…This statement was announced in [29] and was based on some general features of the Husimi function. We give a completely different, purely analytic proof here.…”

Section: Introductionmentioning

confidence: 99%

A transformational property of the Husimi function and its relation to the wigner function and symplectic tomograms

Andreev

Davidović

et al. 2011

Theor Math Phys

View full text Add to dashboard Cite

show abstract

“…В работе [29] показано, что если λ 2 1 и Q(q, p) -функция Хусими, то и Q λ (q, p) тоже является функцией Хусими некоторого физиче-ского состояния. В приложении к настоящей статье дано новое доказательство этого факта.…”

Section: преобразования функции хусими и функции вигнераunclassified

“…В работе [29] этот факт продемонстрирован на примере первого возбужденного состояния осциллятора. К функции Вигнера этого состояния применялось преобра-зование (14), а к получившейся функции W λ (q, p) -преобразование (4), переводящее функцию Вигнера в функцию Хусими.…”

Section: преобразования функции хусими и функции вигнераunclassified