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Introduction

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1992)

Abstract

A non-commutative harmonic oscillator (NCHO for short) is the Weyl-quantization a w(x,D) of an N × N system of the form a(x,ξ) = a2(x,ξ)+a0, (x,ξ ) ε \( \mathbb{R}^n \times \mathbb{R}^n = T^\ast \mathbb{R}^n \), where a2(x,ξ ) is an N×N matrix whose entries are homogeneous polynomials of degree 2 in the (x,ξ ) variables, and a 0 is a constant N×N matrix. In other words, a NCHO is the Weyl-quantization of a matrix-valued quadratic form in (x,ξ ), plus a constant matrix term.

Keywords

  • Harmonic Oscillator
  • Large Eigenvalue
  • Maslov Index
  • Polynomial Differential System
  • Spectral Zeta Function

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Correspondence to Alberto Parmeggiani .

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© 2010 Springer Berlin Heidelberg

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Parmeggiani, A. (2010). Introduction. In: Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction. Lecture Notes in Mathematics(), vol 1992. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11922-4_1

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