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Dynamically Equivalent & Kinematically Distinct Pseudo-Hermitian Quantum Systems

Explores the motivation, classical limit, and perturbative determination of metric operators in pseudo-Hermitian quantum systems. Investigates the geometry of phase space in classical mechanics versus Hilbert space in quantum mechanics. Discusses the concept of separable Hilbert space and symmetry in quantum formulation. Considers different representations for various systems.

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Dynamically Equivalent & Kinematically Distinct Pseudo-Hermitian Quantum Systems

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  1. Dynamically Equivalent & Kinematically Distinct Pseudo-Hermitian Quantum Systems Ali Mostafazadeh Koç University

  2. Outline - Motivation • Pseudo-Hermitian QM & ItsClassical Limit • Indefinite-Metric QM& the C-operator • Perturbative Determination of the Most General Metric Operator • Imaginary Cubic Potential • QM ofKlein-Gordon Fields • Conclusion

  3. In Classical Mechanics the geometry of the phasespace is fixed. In Quantum Mechanics thegeometry of the Hilbert Space is fixed. Is this absolutism justified in QM?

  4. Answer:Yes, because up tounitary-equivalencethere is a single separable Hilbert space.

  5. Though these representations are equivalent, the very fact that they exist reveals a symmetry of the formulation of QM.Different reprsentations may prove appropriate for different systems.

  6. Classical Phase Space Orbits ofImaginary Cubic Potential

  7. QM of Klein-Gordon Fields

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