Major overhaul: All sections have been changed and improved.
Added: Computation of the condensate fraction
Added: Discussion and plots of correlation function and momentum distribution
Added: Section on numerical computation
Added: Appendices on functional analysis
Added: Detailed analysis of the operator K_e
Change: Parameters for numerical simulations.
Change: Renamed "Simplified approach" to "Lieb's simplified approach"
Added: More bibliography
Added: Acknowledgements
Added: Discussion of uniqueness of the solution of the Simple Equation
Added: Exercise: prove \psi_0>=0 using |\psi_0|
Added: Links in bibliography
Removed: Commented blocks
Fixed: Formatting
