Expansions

Energy expansion, unit of energy $\hbar^2/2ma_{1D}^2$:

$$\begin{array}{\vert c\vert c\vert c\vert c\vert c\vert} \hline te... ...)^2}{12}&\displaystyle n\vert a_{1D}\vert&\displaystyle &\\ \hline \end{array}$$

Expansion of the chemical potential, unit of energy $\hbar^2/2ma_{1D}^2$:

$$\begin{array}{\vert c\vert c\vert c\vert c\vert c\vert} \hline te... ...displaystyle \frac{8\pi^2}{3} (na_{1D})^3&\displaystyle &\\ \hline \end{array}$$

The frequency of the oscillations $\frac{\omega^2}{\omega_z^2} =4(1+\triangle\omega)$

$$\begin{array}{\vert l\vert c\vert} \hline $limit$&\displaystyle \... ...e \frac{32\sqrt{2}}{15\pi^2} \frac{\sqrt{N}a_{1D}}{a_{z}}\\ \hline \end{array}$$

Speed of sound in units of $m/\pi\hbar n$

$$\begin{array}{\vert c\vert c\vert c\vert c\vert c\vert} \hline te... ...}{2}&\displaystyle \frac{1}{\pi^2na_{1D}}&\displaystyle &\\ \hline \end{array}$$

Energy and chemical potential (LDA) in units of $N\hbar\omega_z$

$$\begin{array}{\vert l\vert c\vert c\vert} \hline $limit$&\display... ...eft(1-\frac{32}{3\pi^2}/\frac{\sqrt{N}a_{1D}}{a_z}\right)\\ \hline \end{array}$$

Size of the condensate and mean $z^2$ in units of $a_z^2$

$$\begin{array}{\vert l\vert c\vert c\vert} \hline $limit$&\display... ...eft(1-\frac{16}{3\pi^2}/\frac{\sqrt{N}a_{1D}}{a_z}\right)\\ \hline \end{array}$$