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Let $f$ a smooth function with compact support defined on$PSL(2,\mathbb{Z}[i]) \backslash PSL(2,\mathbb{C})$, we prove a formula for theMellin transform of $f$, then we can define the micro-local lift$d\epsilon_{it}$ to $SL(2,\mathbb{C})$. We calculate $(f,d\epsilon_{it})$ for$f$ a cuspidal form and for $f$ an incomplete Eisenstein series. We alsoestablish asymptotic estimates when $t$ tends to $\infty$. We conjecture that anew positive distribution $d\epsilon_{it}^F$, constructed with the Friedrichs'symmetrization technique, satisfies the same asymptotic estimates that$d\epsilon_{it}$. This would imply the quantum ergodicity for Eisenstein serieson $PSL(2,\mathbb{Z}[i]) \backslash PSL(2,\mathbb{C})$

A note on Mellin transform, Eisenstein Series and distribution $d\epsilon_{it}$ on $PSL(2,\mathbb{Z}[i]) \backslash PSL(2,\mathbb{C})$