Making space for harmonic oscillators

Michelotti, Leo ; /Fermilab

Fermi National Accelerator Laboratory

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

DOI  :  10.2172/15017029
RP-ID  :  FERMILAB-FN-0759
RP-ID  :  AC02-76CH03000
RP-ID  :  15017029

美国|英语

来源: UNT Digital Library

【 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.