Exact solution of $D_N$ type quantum Calogero model through a mapping to free harmonic oscillators

Details Exact solution of $D_N$ type quantum Calogero model through a mapping to free harmonic oscillators Exact solution of $D_N$ type quantum Calogero model through a mapping to free harmonic oscillators

2010-12-20

arxiv.org/abs/1012.4342v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

16 pages

Scientific paper

We solve the eigenvalue problem of the $D_N$ type of Calogero model by mapping it to a set of decoupled quantum harmonic oscillators through a similarity transformation. In particular, we construct the eigenfunctions of this Calogero model from those of bosonic harmonic oscillators having either all even parity or all odd parity. It turns out that the eigenfunctions of this model are orthogonal with respect to a nontrivial inner product, which can be derived from the quasi-Hermiticity property of the corresponding conserved quantities.

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