The Harmonic Oscillator in the Plane and the Jordan-Schwinger Algebras
Rabin Banerjee, Pradip Mukherjee
Abstract
The direct and indirect Lagrangian representations of the planar harmonic oscillator have been discussed. The reduction of these Lagrangians in their basic forms characterising either chiral, or pseudo - chiral oscillators have been given. A Hamiltonian analysis, showing its equivalence with the Lagrangian formalism has also been provided. Finally, we show that the chiral and pseudo - chiral modes act as dynamical structures behind the Jordan - Schwinger realizations of the SU(2) and SU(1,1) algebras. Also, the SU(1,1) construction found here is different from the standard Jordan - Schwinger form.
Create a lesson
Related papers
An entangling Hubbard quasiparticle collider on a digital quantum processor
Chan Bin Bark, Hanbyul Kim, Yoonil Koo et al.
A Warped Born Rule Turns an Observer into a Maxwell's Demon
Olumakinde Ogunnaike
A scalable sample-based quantum diagonalization solver for general Pauli-sum Hamiltonians
Yutaro Iiyama
Quantum Query Complexity of Maximum Degree and its Generalizations
Amin Shiraz Gilani, Nikhil S. Mande, Subhasree Patro et al.
Maximally antiflat fixed-particle-number fermionic states
Rahul Gupta, Arya Haghighian, James D. Whitfield
An Annealing-based Quantum Neural Network with Discrete Wavelet Transforms for Enhanced Air Pollution Nowcasting
Otto Menegasso Pires, André Saimon, Daniela Herrmann et al.