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arXiv · 2401.13833

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

Robert J. Ragan·Asaad R. Sakhel·William J. Mullin
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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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Robert J. Ragan, Asaad R. Sakhel, William J. Mullin. 2024-01-24. The Gross-Pitaevskii equation for a infinite square-well with a delta-function barrier. https://arxiv.org/abs/2401.13833

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