Investigating the Spectral Geometry of a Soft Wall Academic Article uri icon

abstract

  • The idealized theory of quantum vacuum energy density is a beautiful application of the spectral theory of differential operators with boundary conditions, but its conclusions are physically unacceptable. A more plausible model of a reflecting boundary that stays within linear spectral theory confines the waves by a steeply rising potential function, which can be taken as a power of one coordinate, z^alpha. We report investigations of this model with considerable student involvement. An exact analytical solution with some numerics for alpha=1 and an asymptotic (semiclassical) analysis of a related problem for alpha=2 are presented.

author list (cited authors)

  • Bouas, J. D., Fulling, S. A., Mera, F. D., Thapa, K., Trendafilova, C. S., & Wagner, J.

complete list of authors

  • Bouas, JD||Fulling, SA||Mera, FD||Thapa, K||Trendafilova, CS||Wagner, J

publication date

  • January 1, 2012 11:11 AM