6533b861fe1ef96bd12c4605
RESEARCH PRODUCT
Modified Landau levels, damped harmonic oscillator and two-dimensional pseudo-bosons
Jean-pierre GazeauFabio BagarelloS. Twareque Alisubject
Solutions of wave equations: bound statesBoson systems[PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]FOS: Physical sciences01 natural sciencesCanonical commutation relationsymbols.namesakedamped harmonic oscillator[MATH.MATH-MP]Mathematics [math]/Mathematical Physics [math-ph]Modified Landau levelQuantum mechanics0103 physical sciences010306 general physicsSettore MAT/07 - Fisica MatematicaMathematical PhysicsHarmonic oscillatorEigenvalues and eigenvectorsLandau levelsBosonMathematical physicsPhysics010308 nuclear & particles physicsStatistical and Nonlinear PhysicsLandau quantizationMathematical Physics (math-ph)harmonic oscillatorssymbolsCoherent statespseudo-bosonsHamiltonian (quantum mechanics)description
In a series of recent papers one of us has analyzed in some details a class of elementary excitations called {\em pseudo-bosons}. They arise from a special deformation of the canonical commutation relation $[a,a^\dagger]=\1$, which is replaced by $[a,b]=\1$, with $b$ not necessarily equal to $a^\dagger$. Here, after a two-dimensional extension of the general framework, we apply the theory to a generalized version of the two-dimensional Hamiltonian describing Landau levels. Moreover, for this system, we discuss coherent states and we deduce a resolution of the identity. We also consider a different class of examples arising from a classical system, i.e. a damped harmonic oscillator.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2010-12-01 |