scholarly journals Vector Constants of Motion for Time-Dependent Kepler and Isotropic Harmonic Oscillator Potentials

2001 ◽  
Vol 31 (2) ◽  
pp. 304-307 ◽  
Author(s):  
O.M. Ritter ◽  
F.C. Santos ◽  
A. C. Tort
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Isotropic Harmonic Oscillator ◽  
Constants Of Motion

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

On the Quantization Problem of a Driven Harmonic Oscillator with Time Dependent Mass and Frequency

2003 ◽  
Vol 17 (18) ◽  
pp. 983-990 ◽  
Author(s):  
Swapan Mandal
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Present Solution ◽  
Quadratic Hamiltonian ◽  
Dependent Mass ◽  
Quantization Problem

The quantization of a driven harmonic oscillator with time dependent mass and frequency (DHTDMF) is considered. We observe that the driven term has no influence on the quantization of the oscillator. It is found that the DHTDMF corresponds the general quadratic Hamiltonian. The present solution is critically compared with existing solutions of DHTDMF.

scholarly journals Time-dependent propagator for an-harmonic oscillator with quartic term in potential

2021 ◽  
Vol 62 (2) ◽  
pp. 023501
Author(s):  
J. Boháčik ◽  
P. Prešnajder ◽  
P. Augustín
Keyword(s):  
Harmonic Oscillator ◽  
Time Dependent ◽  
Quartic Term
Sign in / Sign up

Export Citation Format

Share Document