For the case (a ightarrow 0) the dimensionless G-P equation is [ -frac{1}{2} tilde{abla}^{2} psi+frac{1}{2} s^{2} psi+=mu

Question:

For the case $a ightarrow 0$ the dimensionless G-P equation is

\[
-\frac{1}{2} \tilde{abla}^{2} \psi+\frac{1}{2} s^{2} \psi+=\mu \psi
\]

which has solution $\psi=\frac{1}{\pi^{3 / 4}} \exp \left(-\frac{1}{2} s^{2}ight)$ with $E /\left(N \hbar \omega_{0}ight)=3 / 2$, i.e. the zero point energy for $N$ particles in the trap.

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