Classical and quantum mechanics of complex hamiltonian systems: An extended complex phase space approach |
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Authors: | R S Kaushal |
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Institution: | 1.Department of Physics, Ramjas College (University Enclave),University of Delhi,Delhi,India;2.Department of Physics & Astrophysics,University of Delhi,Delhi,India |
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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}
$
\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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Keywords: | |
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