The Gross-Pitaevskii equation for a infinite square-well with a delta-function barrier

• URL: http://arxiv.org/abs/2401.13833v2
• Date: Tue, 25 Jun 2024 18:51:49 GMT
• Title: The Gross-Pitaevskii equation for a infinite square-well with a delta-function barrier
• Authors: Robert J. Ragan, Asaad R. Sakhel, William J. Mullin,
• Abstract summary: We find solutions that have the symmetry of the non-interacting Hamiltonian as well as asymmetric solutions. We present a variational approximation to the asymmetric state as well as an approximate numerical approach.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The Gross-Pitaevskii equation is solved by analytic methods for an external double-well potential that is an infinite square well plus a $\delta$-function central barrier. We find solutions that have the symmetry of the non-interacting Hamiltonian as well as asymmetric solutions that bifurcate from the symmetric solutions for attractive interactions and from the antisymmetric solutions for repulsive interactions. We present a variational approximation to the asymmetric state as well as an approximate numerical approach. Stability of the states is briefly considered.

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