谐振子模型中热力学量与测不准关系外文.pdfVIP

Results in Physics 6 (2016) 946–951 Contents lists available at ScienceDirect Results in Physics journal homepage: www.jo /results-in-physics Linkage between thermodynamic quantities and the uncertainty relation in harmonic oscillator model Shoichi Nagata Department of Applied Sciences, Muroran Institute of Technology, 27-1 Mizumoto-cho, Muroran, Hokkaido 050-8585, Japan a r t i c l e i n f o a b s t r a c t Article history: The Heisenberg uncertainty relation, DxDpx P⁄/2 (⁄ h/2p), is well known. The purpose of this paper is Received 16 September 2016 to study a linkage between macroscopic thermodynamic quantities and the uncertainty relation. To sim- Received in revised form 1 November 2016 plify matters, we consider one-dimensional harmonic oscillator model. The calculations are carried out Accepted 3 November 2016 by two steps. First, the thermal average of the uncertainty relation is obtained for canonical system in Available online 9 November 2016 thermal equilibrium at temperature T, which is denoted by ðDxÞ ðDp Þ . Second, the thermodynamic T x T quantities are expressed analytically as a function of ðDxÞ ðDp Þ within the harmonic oscillator model. T x T