Classical and quantum mechanics of complex

Hamiltonian systems: An extended complex

phase space approach

R S KAUSHAL^1,2

¹Department of Physics, Ramjas College (University Enclave), University of Delhi,

Delhi 110 007, India

²Department of Physics {\&} Astrophysics, University of Delhi, Delhi 110 007, India

E-mail: rkaushal@physics.du.ac.in

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 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.

Keywords. Complexification methods; complex Lagrangian; Chevreul

pendulum; generalized Hamilton's principle.

PACS Nos 02.90.+p; 03.20.+I; 03.65.Ge