Abstract
Non-relativistic bosons interacting with Coulomb forces are unstable, as Dyson showed 20 years ago, in the sense that the ground state energy satisfiesE 0≦−AN 7/5. We prove that 7/5 is the correct power by proving thatE 0≧−BN 7/5. For the non-relativistic bosonic, one-component jellium problem, Foldy and Girardeau showed thatE 0≦−CNρ1/4. This 1/4 law is also validated here by showing thatE 0≧−DNρ1/4. These bounds prove that the Bogoliubov type paired wave function correctly predicts the order of magnitude of the energy.
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Communicated by A. Jaffe
Work partially supported by U.S. National Science Foundation grant DMS 8600748
Work partially supported by U.S. National Science Foundation grant PHY85-15288-A01
Work supported by Alfred Sloan Foundation dissertation fellowship
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Conlon, J.G., Lieb, E.H. & Yau, HT. TheN 7/5 law for charged bosons. Commun.Math. Phys. 116, 417–448 (1988). https://doi.org/10.1007/BF01229202
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DOI: https://doi.org/10.1007/BF01229202