Operadic Lax representations for the harmonic oscillator are used to construct the quantum counterparts of some 3d real Lie algebras in Bianchi classification. The Jacobians of these quantum algebras arecalculated. It is conjectured that the tangent algebras of these quantum algebras are the Heisenberg algebra. From this it follows that the volume element in R has discrete values: |(x, y, z)| = 4 √ 2(2n+ 1) (n = 0, 1, 2, . . . ).