Gross–Pitaevskii Equation for Bose–Einstein Condensation

Application ID: 52221

This tutorial model solves the Gross–Pitaevskii Equation for the ground state of a Bose–Einstein condensate in a harmonic trap, using the Schrödinger Equation physics interface in the Semiconductor Module. The equation is essentially a nonlinear single-particle Schrödinger Equation, with a potential energy contribution proportional to the local particle density. The eigenvalue study is not suitable for solving this kind of nonlinear eigenvalue problems. Instead, a stationary study is used with a global equation enforcing the normalization of the wave function to solve for the ground state solution. The result for a large number of particles compares well with the Thomas–Fermi approximation as expected.

This model example illustrates applications of this type that would nominally be built using the following products:

Semiconductor Module