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

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      https://www.ias.ac.in/article/fulltext/pram/073/02/0287-0297

    • Keywords

       

      Complexification methods; complex Lagrangian; Chevreul pendulum; generalized Hamilton’s principle.

    • 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 $\mathcal{PT}$ 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.

    • Author Affiliations

       

      R S Kaushal1 2

      1. Department of Physics, Ramjas College (University Enclave), University of Delhi, Delhi 110 007, India
      2. Department of Physics & Astrophysics, University of Delhi, Delhi 110 007, India
    • Dates

       
  • Pramana – Journal of Physics | News

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