Making space for harmonic oscillators

[摘要] If we restrict the number of harmonic oscillator energy eigenstates to some finite value, N, then the discrete spectrum of the corresponding position operator comprise the roots of the Hermite polynomial H{sub N+1}. Its range is just large enough to accommodate classical motion at high energy. A negative energy term must be added to the Hamiltonian which affects only the last eigenstate, |N>, suggesting it is concentrated at the extrema of this finite ''space''. Calculations support a conjecture that, in the limit of large N, the global distribution of points approaches the differential form for classical action.

[发布日期] 2004-11-01 [发布机构] Fermi National Accelerator Laboratory

[关键词] Theory-Hep;Position Operators Theory-Hep;Hermite Polynomials;72 Physics Of Elementary Particles And Fields;Harmonic Oscillators