For every genuine irreducible admissible smooth representation ħ of the metaplectic group Šp(2n) over a p-adic field, and every smooth oscillator representation wψ of Šp(2n), we prove that the tensor product ħ ⊗wŠis multiplicity free as a smooth representation of the symplectic group Sp(2n). Similar results are proved for general linear groups and unitary groups.