Abstract
Non-relativistic bosons interacting with Coulomb forces are unstable, as Dyson showed 20 years ago, in the sense that the ground state energy satisfies E 0 ≦ — AN 7/5. We prove that 7/5 is the correct power by proving that E 0 ≧ — BN 7/5. For the non-relativistic bosonic, one-component jellium problem, Foldy and Girardeau showed that E 0 ≦ — CN ρ 1/4. This 1/4 law is also validated here by showing that E 0 ≧ — DN ρ 1/4. These bounds prove that the Bogoliubov type paired wave function correctly predicts the order of magnitude of the energy.
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. (1997). The N 7/5 Law for Charged Bosons. In: Thirring, W. (eds) The Stability of Matter: From Atoms to Stars. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-03436-1_46
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