Rabin Banerjee, Pradip Mukherjee
We show that the elementary modes of the planar harmonic oscillator can be quantised in the framework of quantum mechanics based on pseudo-hermitian hamiltonians. These quantised modes are demonstrated to act as dynamical structures behind a new Jordan – Schwinger realization of the SU(1,1) algebra. This analysis complements the conventional Jordan – Schwinger construction of the SU(2) algebra based on hermitian hamiltonians of a doublet of oscillators.
http://arxiv.org/abs/1410.4678
Quantum Physics (quant-ph); High Energy Physics – Theory (hep-th)
Rabin Banerjee, Pradip Mukherjee
We provide a reduction of a set of two coupled oscillators with balanced loss and gain in their elementary modes. A possible method of quantization based on these elementary modes, in the framework of PT symmetric quantum mechanics is indicated.
http://arxiv.org/abs/1408.5038
High Energy Physics – Theory (hep-th)
B. Bagchi, A. Banerjee, A. Ganguly
This paper examines the features of a generalized position-dependent mass Hamiltonian in a supersymmetric framework in which the constraints of pseudo-Hermiticity and CPT are naturally embedded. Different representations of the charge operator are considered that lead to new mass-deformed superpotentials which are inherently PT-symmetric. The qualitative spectral behavior of the Hamiltonian is studied and several interesting consequences are noted.
http://arxiv.org/abs/1212.2122
Quantum Physics (quant-ph); High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph)
B. Bagchi, A. Ghose Choudhury, Partha Guha
We explore the Jacobi Last Multiplier as a means for deriving the Lagrangian of a fourth-order differential equation. In particular we consider the classical problem of the Pais-Uhlenbeck oscillator and write down the accompanying Hamiltonian. We then compare such an expression with an alternative derivation of the Hamiltonian that makes use of the Ostrogradski’s method and show that a mapping from the one to the other is achievable by variable transformations. Assuming canonical quantization procedure to be valid we go for the operator version of the Hamiltonian that represents a pair of uncoupled oscillators. This motivates us to propose a generalized Pais-Uhlenbeck Hamiltonian in terms of the usual harmonic oscillator creation and annihilation operators by including terms quadratic and linear in them. Such a Hamiltonian turns out to be essentially non-Hermitian but has an equivalent Hermitian representation which is reducible to a typically position-dependent reduced mass form.
http://arxiv.org/abs/1212.2092
Mathematical Physics (math-ph); Quantum Physics (quant-ph)