8 Crypto Exotic Oscillator and Pt Symmetry
نویسنده
چکیده
We study complexified Harmonic Oscillator with a position dependent mass, referred to in the present paper as Exotic Oscillator (EO), in arbitrary dimensions. The real space EO has an interesting dynamics: in the equation of motion the full Hamiltonian operator appears in place of the frequency parameter in a Harmonic Oscillator. We reveal some generic features in the constraint structure of these Crypto-gauge invariant models. Lastly we discuss the classical trajectories of complexified EO for real energy, concentrating on the PT -symmetry aspect. We utilize the formalism developed by Smilga [6] who exploited the ”Crypto”-gauge invariance of the complexified models to generate trajectories, in the context of anharmonic ocillators. It was shown in [6] that the dynamics of Crypto-oscillators were same as that of the complex oscillators, for PT -symmetric models. The similar phenomenon can be tested for the Crypto EO model presented here. subir [email protected] [email protected]
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Crypto-Harmonic Oscillator in Higher Dimensions: Classical and Quantum Aspects
We study complexified Harmonic Oscillator models in two and three dimensions. Our work is a generalization of the work of Smilga [4] who initiated the study of these Crypto-gauge invariant models that can be related to PT -symmetric models. We show that rotational symmetry in higher spatial dimensions naturally introduces more constraints, (in contrast to [4] where one deals with a single const...
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