Harmonic-trap energy-zero convention
= Harmonic-trap energy-zero convention
The exact three-dimensional oscillator ground <energy> is $3\hbar\omega/2$ above the potential minimum. Subtracting it sets the condensate <energy> to zero. The commonly used $g(\epsilon)=\epsilon^2/[2(\hbar\omega)^3]$ is the leading continuum term; it does not include the finite-level corrections from shifting the <energy> origin.