Summary
The sensitivity of the spectral density and the correlation of the harmonic oscillator to the charge distribution is examined in the context of classical stochastic electrodynamics. While the first exhibits some degree of sensitivity, the second exhibits none in the limit of zero charge. Thus a comparison can be made with nonrelativistic quantum mechanics independent of the charge distribution. In the same spirit, the anharmonic oscillator is examined. In the limit of zero charge, it is shown that classical stochastic electrodynamics qualitatively agrees with quantum mechanics, but ambiguities make a quantitative comparison difficult. In an appendix, the oscillator approximation to the hydrogen atom is briefly discussed.
Riassunto
La sensibilità della densità spettrale e della correlazione tra oscillatore armonico e distribuzione di carica è esaminata nel contesto dell’elettrodinamica stocastica classica. Mentre la prima mostra alcuni gradi di sensibilità, la seconda non ne mostra alcuno nel limite della carica nulla. Così si può fare un confronto con la meccanica quantistica non relativistica indipendentemente dalla distribuzione delle cariche. Nello stesso spirito, si esamina l’oscillatore anarmonico. Nel limite di carica nulla, si mostra che l’elettrodinamica stocastica classica è in accordo dal punto di vista qualitativo con la meccanica quantistica, mentre ambiguità rendono difficile un confronto quantitativo. Nell’appendice si discute brevemente l’approssimazione dell’oscillatore rispetto all’atomo d’idrogeno.
Резюме
В контексте классической стохастической электродинамики исследуется чувствительность спектральной плотности и корреляции гармонического осциллятора к распределению заряда. Тогда как спектральная плотность обнаруживает некоторую степень чувствительности, корреляция не проявляет никакой чувствительности в пределе нулевого заряда. Следовательно, сравнение может быть проведено в рамках нерелятивистской квантовой механики независимо от распределения заряда. Таким же образом исследуется ангармонический осциллятор. В пределе нулевого заряда показывается, что классическая стохастическая электродинамика качественно согласуется с квантовой механикой, но неопределенности делают количественное сравнение затруднительным. В приложении вкратце обсуждается осцилляторное приближение для атома водорода.
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Moore, S.M., Ramírez, J.A. The harmonic and anharmonic oscillator in classical stochastic electrodynamics. Nuov Cim B 64, 275–286 (1981). https://doi.org/10.1007/BF02903289
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DOI: https://doi.org/10.1007/BF02903289