Solution of Coulomb path integral in momentum space |
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| Affiliation: | 1. National Engineering Laboratory for Clean Technology of Leather Manufacture, Sichuan University, Chengdu 610065, China;2. Key Laboratory of Coastal Environmental Processes and Ecological Remediation, Yantai Institute of Coastal Zone Research, Chinese Academy of Sciences, Yantai 264003, China;3. School of Chemistry and Chemical Engineering, Yantai University, Yantai 264005, China;1. Department of Mechanical Engineering, University of Michigan, MI 48109-2125, United States;2. Department of Materials Science & Engineering, University of Michigan, MI 48109-2125, United States;1. School of Mathematics and Physics, Nanjing Institute of Technology, Nanjing 211167, PR China;2. Industrial Center, Nanjing Institute of Technology, Nanjing 211167, PR China;3. Department of Mathematics, Nanjing University, Nanjing 210093, PR China;4. School of Mathematics and Statistics, Zaozhuang University, Zaozhuang, 277160, PR China |
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| Abstract: | The path integral for a point particle in a Coulomb potential is solved in momentum space. The solution permits us to answer for the first time an old question of quantum mechanics in curved spaces raised in 1957 by DeWitt: The Hamiltonian of a particle in a curved space must not contain an additional term proportional to the curvature scalar R, since this would change the level spacings in the hydrogen atom. |
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