Non-relativistic bosons interacting with Coulomb forces are unstable, as Dyson showed 20 years ago, in the sense that the ground state energy satisfies E0≦-AN7/5. We prove that 7/5 is the correct power by proving that E0≧-BN7/5. For the non-relativistic bosonic, one-component jellium problem, Foldy and Girardeau showed that E0≦-CNρ1/4. This 1/4 law is also validated here by showing that E0≧-DNρ1/4. These bounds prove that the Bogoliubov type paired wave function correctly predicts the order of magnitude of the energy.
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Physics and Astronomy(all)
- Mathematical Physics