A Scaling Law for the Energy Levels of a Nonlinear Schrodinger Equation

Abstract

It is shown that the energy levels of the one-dimensional nonlinear Schrodinger, or Gross-Pitaevskii, equation with the homogeneous trap potential $x^{2p}$, $p\ge 1$, obey an approximate scaling law and as a consequence the energy increases approximately linearly with the quantum number. Moreover, for a quadratic trap, $p=1$, the rate of increase of energy with the quantum number is independent of the nonlinearity: this prediction is confirmed with numerical calculations. It is also shown that the energy levels computed using a variational approximation do not satisfy this scaling law.

10 pages, 4 figures. Submitted to J. Phys. B

References in corpus (1)

• Non-Ground-State Bose-Einstein Condensates of Trapped Atoms

Cited by in corpus (2)

• Basics of Bose-Einstein Condensation
• Highly Accurate Critical Exponents from Self-Similar Variational Perturbation Theory