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arXiv · 2110.12082

Example Exact Solutions of the Time-independent Gross-Pitaevskii and Schr\"odinger Equations

Bhavika Bhalgamiya·M. A. Novotny
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Abstract

A prescription is given to obtain some exact results for certain external potentials $V\left({\vec r}\right)$ of the time-independent Gross-Pitaevskii and Schr\"odinger equations. The study motivation is the ability to program $V\left({\vec r}\right)$ experimentally in Bose-Einstein condensates. Rather than derive wavefunctions that are solutions for a given $V\left({\vec r}\right)$, we ask which $V\left({\vec r}\right)$ will have a given pdf (probability density function) $P\left({\vec r}\right)$. Several examples in 1D and 2D are presented for well-known pdfs and for the hydrogen atom in momentum space.

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Bhavika Bhalgamiya, M. A. Novotny. 2021-10-22. Example Exact Solutions of the Time-independent Gross-Pitaevskii and Schr\"odinger Equations. https://arxiv.org/abs/2110.12082

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