2003/10/09 by H. -J. Stoeckmann, H-J Stöckmann · 7 citations
Chemistry · Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Constant (computer programming) #Coupling (piping) #Coupling constant #Eigenfunction #Eigenvalues and eigenvectors #Gaussian #Harmonic #Harmonic oscillator #Mathematical analysis #Mathematical physics #Mathematics #Matrix (chemical analysis) #Molecular spectroscopy and chirality #Physics #Quantum mechanics #Random Matrices and Applications #Random matrix #Schrödinger equation #cond-mat.stat-mech #math-ph #math.MP #quant-ph
paper · pdf · doi:10.1088/0305-4470/37/1/009
published in Journal of Physics A Mathematical and General 37(1), 137-146 (Institute of Physics) · accepted by J. Phys. A
arxiv created 2003/10/09 · openalex publication_date 2003/12/09 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
From random matrix theory it is known that for special values of the coupling constant the Calogero–Moser (CM) equation system is nothing but the radial part of a generalized harmonic oscillator Schrödinger equation. This allows an immediate construction of the solutions by means of a Rodriguez relation. The results are easily generalized to arbitrary values of the coupling constant. By this the CM equations become nearly trivial. As an application an expansion for ⟨e iTr( XY ) ⟩ in terms of eigenfunctions of the CM equation system is obtained, where X and Y are matrices taken from one of the Gaussian ensembles, and the brackets denote an average over the angular variables.