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Variation of single-particle occupations and the uncertainty principle
Affiliation:1. Baicheng Normal University, Baicheng 137000, PR China;2. Institute of Green Chemistry and Chemical Technology, School of Chemistry and Chemical Engineering, Jiangsu University, Zhenjiang 212013, PR China;1. School of Environmental Science and Engineering, Hebei University of Science and Technology, Shijiazhuang 050018, China;2. School of Chemical Sciences and National Engineering Laboratory for VOCs Pollution Control Material & Technology, Research Center for Environmental Material and Pollution Control Technology, University of Chinese Academy of Sciences, Beijing 100049, China;3. College of Textile and Garments, Textile and Garment Technology Innovation Center, Hebei University of Science and Technology, Shijiazhuang 050018, China;4. School of Chemical Engineering, Hebei University of Technology, Tianjin 300401, China;1. Department of Chemistry, Turabah University College, Taif University, P.O.Box 11099, Taif 21944, Saudi Arabia;2. Department of Chemistry, Faculty of Sciences, Al-Azhar University, P.O. Box 11754, Nasr City, Cairo, Egypt;3. Ministry of Environment, Egyptian Environmental Affair Agency, 30 Misr Helwan El-Zyrae Road, Maadi, Cairo, Egypt;4. Department of Chemistry Sciences College, Turabah Branch, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia;5. Department of Teaching and Learning, College of Education and Human Development, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia;6. Faculty of Science and Technology, Madhyanchal Professional University, Ratibad, Bhopal 462044, India;7. Environmental and Atmospheric Sciences Research Group, Scientific Research Center, Al-Ayen University, Nasiriyah 64001, Thi-Qar, Iraq;8. Electrical Engineering Department, College of Engineering, King Khalid University, Abha 61421, Saudi Arabia;9. Department of Chemistry, University of Ha’il, Ha’il 81441, Saudi Arabia;1. College of Chemistry and Chemical Engineering, Hunan University, Changsha 410082, PR China;2. College of Environmental Science and Engineering, Hunan University, Lushan South Road, Yuelu District, Changsha 410082, PR China;3. State Key Laboratory of Chemo/Biosensing and Chemometrics, Hunan University, Changsha 410082, PR China
Abstract:A relation between a temporal variation of the occupation of a single-particle state and the uncertainty of a single-particle energy is derived. The analogous space-momentum uncertainty principle provides a lower bound for the kinetic energy density. The bound has the form of the von Weizsäcker correction to the ground-state Thomas-Fermi energy density.
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