A study of coherent states for a charged oscillator in electric and magnetic fields.

In the present work a suitable Canonical Transformation for the problem of a Charged Oscillator in Crossed Electric and Magnetic Fields was set. by mean of this Canonical Transformation the Coherent States for a Charged Oscillator in Crossed Electric and Magnetic Field are constructed. Some applications of these Coherent States have been performed. Among these applications, the classical limit of
the problems of a Charged Oscillator in Crossed Electric and Magnetic Fields were dealt with by using the mentioned constructed Coherent State. (a) It is found that the classical limit of the problem a Charged Oscillator in Crossed Electric and Magnetic Fields is statisical in nature (b) Other applications involve the derivation of Continuity Equation and the Euler Equations of hydrodynamics for the problem of a
Charged Oscillator in Crossed Electric and Magnetic Fields. Our success in deriving the Continuity Equation for the latter mentioned system confirms that the law of conservation of Probability Density is satisfied for this system. Furthermore, our success in constructing the Euler Equations of hydrodynamics for the under consideration system confirms that the hydrodynamical ideas are satisfied for this system. III. The Density Operator in terms of the Q-representation for the Coherent States of the problems of a Charged Oscillator in a Magnetic Field and a Charged Oscillator in Crossed Electric and Magnetic Fields was also constructed. The behavior of the Q-functions for these problems was studied in phase-space. This was achieved by using a Computer Visualization Method. Some important results followed from using the mentioned Computer Visualization for Coherent States for the problems under consideration. An important one was that it is found that the Q-functions for such mentioned problems represent Gaussians that follow the classical trajectory of these problems in phase-space. Finally, it should be mentioned that in the present work a mathematical analogy between the problems of a Charged Oscillator in Crossed Electric and Magnetic Fields and the problem of a Cranked Shifted Harmonic Oscillator, which is used in Nuclear Physics, was observed. This mathematical analogy has importance when one deals with the problem of a Cranked Shifted Oscillator, where all equations constructed in the present work and other results obtained for the Charged Oscillator in Crossed Electric and Magnetic Fields system can be transformed by mean of this mathematical analogy to describe the Cranked Shifted Oscillator system.