Eigenfunctions for SU(N) particles with 1/r^2 interaction in harmonic confinement

Abstract

We find a set of the exact eigenfunctions which provide the energy spectrum for the quantum $N$-body Calogero-Sutherland model for fermions or bosons with SU($\nu$) spin degrees of freedom moving in a harmonic confinement potential. The eigenfunctions are explicitly constructed as a simple product of the Jastrow wave function for the ground state and the Hermite polynomials introduced to generate the excited states. The corresponding energy spectrum is given by a sum of the correlated ground-state energy and of the excited-state energy for SU($\nu$) free particles in a harmonic well.

10pages Latex

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Cited by in corpus (13)

• Exact Quantum Decay of an Interacting Many-Particle System: the Calogero-Sutherland model
• Multicomponent Calogero Model of $B_N$-Type Confined in Harmonic Potential
• Integrable $1/r^2$ Spin Chain with Reflecting End
• Integrable families of hard-core particles with unequal masses in a one-dimensional harmonic trap
• Calogero-Sutherland Type Models in Higher Dimensions
• Truncated Calogero-Sutherland models
• Exact ground states of quantum many-body systems under confinement
• Connection between Calogero-Marchioro-Wolfes type few-body models and free oscillators
• Nonadiabatic energy fluctuations of scale-invariant quantum systems in a time-dependent trap
• One-Dimensional Quantum Systems with Ground-State of Jastrow Form Are Integrable
• Bosonic and fermionic single-particle states in the Haldane approach to statistics for identical particles
• Echoes and defects in the Calogero model
• Parent Hamiltonians of Jastrow Wavefunctions