Oscillator representations and systems of ordinary differential equations.

@article{Parmeggiani2001OscillatorRA,
  title={Oscillator representations and systems of ordinary differential equations.},
  author={A. Parmeggiani and M. Wakayama},
  journal={Proceedings of the National Academy of Sciences of the United States of America},
  year={2001},
  volume={98 1},
  pages={
          26-30
        }
}
  • A. Parmeggiani, M. Wakayama
  • Published 2001
  • Physics, Medicine
  • Proceedings of the National Academy of Sciences of the United States of America
  • Using representation-theoretic methods, we determine the spectrum of the 2 x 2 system. Q(x, D(x)) = A- partial differential(2)(x)2 + x(2)2 + Bx partial differential(x) + 1/2, x in, with A, B in Mat(2)(R) constant matrices such that A = (t)A > 0 (or <0), B = -(t)B not equal 0, and the Hermitian matrix A + iB positive (or negative) definite. We also give results that generalize (in a possible direction) the main construction. 
    45 Citations

    Topics from this paper.

    Finite Lifetime Eigenfunctions of Coupled Systems of Harmonic Oscillators
    On the essential spectrum of certain non-commutative oscillators
    • 2
    • PDF
    Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction
    • 32
    • PDF
    Zeta Functions for the Spectrum of the Non-Commutative Harmonic Oscillators
    • 32

    References

    SHOWING 1-9 OF 9 REFERENCES
    Positivity of a system of differential operators
    • 7
    • PDF
    Non-Commutative Harmonic Oscillators I, preprint
    • 1998
    Non-Abelian Harmonic Analysis
    • 151
    ON MELIN'S INEQUALITY FOR SYSTEMS
    • 15
    On Certain Systems of Differential Equations Associated with Lie-Algebra Representations and Their Perturbations
    • 2000
    Ph
    • 1989