scholarly journals FOUR KINDS OF RAISING AND LOWERING-OPERATORS OF A TWO-DIMENSIONAL-ISOTROPIC HARMONIC OSCILLATOR

1997 ◽  
Vol 46 (3) ◽  
pp. 423
Author(s):  
LIU YU-FENG ◽  
ZENG JIN-YAN
Keyword(s):  
Harmonic Oscillator ◽  
Two Dimensional ◽  
Raising And Lowering Operators ◽  
Isotropic Harmonic Oscillator ◽  
Lowering Operators

Two-dimensional isotropic harmonic oscillator approach to classical and quantum Stokes parameters

2004 ◽  
Vol 82 (10) ◽  
pp. 767-773 ◽  
Author(s):  
R D Mota ◽  
M A Xicoténcatl ◽  
V D Granados
Keyword(s):  
Harmonic Oscillator ◽  
Classical Limit ◽  
Plane Electromagnetic Wave ◽  
Stokes Parameters ◽  
Two Dimensional ◽  
Expectation Value ◽  
Isotropic Harmonic Oscillator ◽  
Pauli Matrices ◽  
Constants Of Motion ◽  
Polarization Matrix

We show that the well-known Stokes operators, defined as elements of the Jordan–Schwinger map with the Pauli matrices of two independent bosons, are equal to the constants of motion of the two-dimensional isotropic harmonic oscillator. Taking the expectation value of the Stokes operators in a two-mode coherent state, we obtain the corresponding classical Stokes parameters. We show that this classical limit of the Stokes operators, the 2 × 2 unit matrix and the Pauli matrices may be used to expand the polarization matrix. Finally, by means of the constants of motion of the classical two-dimensional isotropic harmonic oscillator, we describe the geometric properties of the polarization ellipse. Our study is restricted to the case of a monochromatic quantized-plane electromagnetic wave that propagates along the z axis.PACS Nos.: 42.50.–p, 42.25.Ja, 11.30.–j

scholarly journals Twisted Conformal Algebra and Quantum Statistics of Harmonic Oscillators

2014 ◽  
Vol 2014 ◽  
pp. 1-4
Author(s):  
J. Naji ◽  
S. Heydari ◽  
R. Darabi
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Statistical Mechanics ◽  
Quantum Statistics ◽  
Conformal Algebra ◽  
Harmonic Oscillators ◽  
Two Dimensional ◽  
Raising And Lowering Operators ◽  
Lowering Operators

We consider noncommutative two-dimensional quantum harmonic oscillators and extend them to the case of twisted algebra. We obtained modified raising and lowering operators. Also we study statistical mechanics and thermodynamics and calculated partition function which yields the free energy of the system.

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