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Classical and quantum mechanics of complex hamiltonian systems: An extended complex phase space approach

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Abstract

Certain aspects of classical and quantum mechanics of complex Hamiltonian systems in one dimension investigated within the framework of an extended complex phase space approach, characterized by the transformation x = x 1 + ip 2, p = p 1 + ix 2, are revisited. It is argued that Carl Bender inducted \( \mathcal{P}\mathcal{T} \) symmetry in the studies of complex power potentials as a particular case of the present general framework in which two additional degrees of freedom are produced by extending each coordinate and momentum into complex planes. With a view to account for the subjective component of physical reality inherent in the collected data, e.g., using a Chevreul (hand-held) pendulum, a generalization of the Hamilton’s principle of least action is suggested.

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Authors and Affiliations

  1. Department of Physics, Ramjas College (University Enclave), University of Delhi, Delhi, 110 007, India

    R. S. Kaushal

  2. Department of Physics & Astrophysics, University of Delhi, Delhi, 110 007, India

    R. S. Kaushal

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Kaushal, R.S. Classical and quantum mechanics of complex hamiltonian systems: An extended complex phase space approach. Pramana - J Phys 73, 287–297 (2009). https://doi.org/10.1007/s12043-009-0120-x

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