scholarly journals The Wigner function negative value domains and energy function poles of the harmonic oscillator

2021 ◽  
Author(s):  
E. E. Perepelkin ◽  
B. I. Sadovnikov ◽  
N. G. Inozemtseva ◽  
E. V. Burlakov
Keyword(s):  
Harmonic Oscillator ◽  
Wigner Function ◽  
Energy Function

scholarly journals Extended Wigner function for the harmonic oscillator in the phase space

2020 ◽  
Vol 19 ◽  
pp. 103546
Author(s):  
E.E. Perepelkin ◽  
B.I. Sadovnikov ◽  
N.G. Inozemtseva ◽  
E.V. Burlakov
Keyword(s):  
Phase Space ◽  
Harmonic Oscillator ◽  
Wigner Function

On the generalization of moyal equation for an arbitrary linear quantization

2021 ◽  
Vol 24 (01) ◽  
pp. 2150003
Author(s):  
Leonid A. Borisov ◽  
Yuriy N. Orlov
Keyword(s):  
Characteristic Function ◽  
Harmonic Oscillator ◽  
Linear Combination ◽  
Stationary Solution ◽  
Wigner Function ◽  
Inverse Operator ◽  
Stationary Solutions ◽  
Weyl Quantization ◽  
Quantization Rule ◽  
Arbitrary Linear Combination

For an arbitrary linear combination of quantizations, the kernel of the inverse operator is constructed. An equation for the evolution of the Wigner function for an arbitrary linear quantization is derived and it is shown that only for Weyl quantization this equation does not contain a source of quasi-probability. Stationary solutions for the Wigner function of a harmonic oscillator are constructed, depending on the characteristic function of the quantization rule. In the general case of Hermitian linear quantization these solutions are real but not positive. We found the representation of Weyl quantization in the form of the limit of a sequence of linear Hermitian quantizations, such that for each element of this sequence the stationary solution of the Moyal equation is positive.

On classical and quantum harmonic potentials

2000 ◽  
Vol 78 (10) ◽  
pp. 937-946 ◽  
Author(s):  
P Mohazzabi
Keyword(s):  
Potential Energy ◽  
Harmonic Oscillator ◽  
Energy Function ◽  
Mechanical Energy ◽  
Energy Levels ◽  
Potential Energy Function ◽  
Quantum Mechanical ◽  
Quantum Mechanical Energy

To date, the only potential energy function that has been demonstrated to be classical harmonic but not quantum harmonic is that of the asymmetrically matched harmonic oscillator. By investigating the accurate quantum mechanical energy levels of the potential V = V0 [Formula: see text], we demonstrate that this is the second member of the class. PACS No.: 03.65Ge

scholarly journals The Wigner function of aq-deformed harmonic oscillator model

2007 ◽  
Vol 40 (20) ◽  
pp. 5427-5441 ◽  
Author(s):  
E I Jafarov ◽  
S Lievens ◽  
S M Nagiyev ◽  
J Van der Jeugt
Keyword(s):  
Harmonic Oscillator ◽  
Wigner Function ◽  
Oscillator Model ◽  
Harmonic Oscillator Model
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