Spectral Properties of the Massless Relativistic Harmonic Oscillator

Jozsef Lorinczi; Jacek Malecki

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arXiv · 1006.3665

Spectral Properties of the Massless Relativistic Harmonic Oscillator

Jozsef Lorinczi·Jacek Malecki

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Abstract

The spectral properties of the pseudo-differential operator $(-d^2/dx^2)^{1/2}+x^2$ are analyzed by a combination of functional integration methods and direct analysis. We obtain a representation of its eigenvalues and eigenfunctions, prove precise asymptotic formulae, and establish various analytic properties. We also derive trace asymptotics and heat kernel estimates.

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BibTeX RIS

Jozsef Lorinczi, Jacek Malecki. 2010-06-18. Spectral Properties of the Massless Relativistic Harmonic Oscillator. https://arxiv.org/abs/1006.3665

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