Two-dimensional isotropic harmonic oscillator

2012 ◽  
pp. 203-207
Author(s):  
Bipin R. Desai
Keyword(s):  
Harmonic Oscillator ◽  
Two Dimensional ◽  
Isotropic Harmonic Oscillator

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

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