## Scale transformations in phase space and stretched states of a harmonic oscillator

Authorized Users Only

##### 2017

##### Authors

Andreev, Vladimir A.Davidović, Dragomir M.

Davidović, Ljubica D.

Davidović, Milos D.

Davidović, Milena

##### Article (Published version)

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Show full item record##### Abstract

We consider scale transformations (q, p) - gt (lambda q, lambda p) in phase space. They induce transformations of the Husimi functions H(q, p) defined in this space. We consider the Husimi functions for states that are arbitrary superpositions of n-particle states of a harmonic oscillator. We develop a method that allows finding so-called stretched states to which these superpositions transform under such a scale transformation. We study the properties of the stretched states and calculate their density matrices in explicit form. We establish that the density matrix structure can be described using negative binomial distributions. We find expressions for the energy and entropy of stretched states and calculate the means of the number-ofstates operator. We give the form of the Heisenberg and Robertson-Schrodinger uncertainty relations for stretched states.

##### Keywords:

phase space / Husimi function / scale transformation / harmonic oscillator / stretched state / uncertainty relation

##### Source:

Theoretical and Mathematical Physics, 2017, 192, 1, 1080-1096##### Publisher:

- Maik Nauka Publishing / Springer SBM

##### Projects:

- Physical Implications of Modified Spacetime (RS-171031)
- A new approach to foundational problems of quantum mechanics related to applications in quantum technologies and interpretations of signals of various origins (RS-171028)

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**DOI: **10.1134/S0040577917070091

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**ISSN: **0040-5779

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**WoS: **000407759300009

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**Scopus: **2-s2.0-85027407589

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