A natural generalization of the irreducible linear representations of compact groups [T. Bröcker, T. tom Dieck, Representations of compact Lie groups. Graduate Texts Math. 98, New York-Berlin-Heidelberg (1985; Zbl 0581.22009)] leads to the unitary representations of unimodular locally compact topological groups which are square integrable modulo their projective kernels. Their coefficient functions satisfy beautiful orthogonality relations [A. Borel, Représentations de groupes localement compacts. Lect. Notes Math. 276 (1972; Zbl 0242.22007); D. S. Shucker, Proc. Am. Math. Soc. 89, 169-172 (1983; Zbl 0523.22006)] which can be traced back to R. Godement [C. R. Acad. Sci., Paris 225, 521-523, 657-659 (1947; Zbl 0029.19906 and 029.19907)]. The unitary representations of nilpotent Lie groups which are square integrable modulo their projective kernels [C. C. Moore and J. A. Wolf, Trans. Am. Math. Soc. 185, 445-462 (1973; Zbl 0274.22016)] admit a useful geometric characterization with applications to quantum holography [W. Schempp, Harmonic analysis on the Heisenberg nilpotent Lie group, with applications to signal theory. Pitman Res. Notes Math. Ser., 147, Harlow, Essex (1986; Zbl 0632.43001)]. The geometric characterization says that exactly the equivalence classes of the square integrable linear representations of dimension \(> 1\) admit planar coadjoint orbits in the dual of the associated Lie algebras [J. Brezin, Geometry and the method of Kirillov. In: J. Carmona, J. Dixmier and M. Vergue (eds.), Non-commutative harmonic analysis, Lect. Notes Math. 466, 13-25, Berlin-Heidelberg-New York (1975; Zbl 0345.22006); R. Felix, Proc. Am. Math. Soc. 86, 151-152 (1982; Zbl 0494.22006)]. The planar coadjoint orbits can be considered as homogeneous spaces equipped with their natural symplectic affine structure which is in accordance with the Kepplerian temporospatial strategy of physical astronomy as exposed by Johannes Keppler in his Mars commentaries of 1609, entitled Astronomia nova [W. Schempp, The structure-function problem of Fourier transform magnetic resonance imaging. John Wiley & Sons, New York, Chichester, Brisbane (in print)]. It is reasonable to regard square integrability as an essential part of the Stone-von Neumann theorem of quantum mechanics. Then the nonlocality phenomenon of quantum mechanics is a consequence of quantum holography [W. Schempp, Geometric analysis: The double-slit interference experiment and magnetic resonance imaging. In: Cybernetics and Systems ‘96, Vol. I., R. Trappl (Ed.), pp. 179-183, Austrian Society for Cybernetic Studies, Vienna 1996]. – The paper under review presents an orthogonality theorem for square integrable representations on homogeneous spaces \(G/H\) associated to a locally compact topological group \(G\) which does not need to be unimodular, modulo a closed subgroup \(H \to G\). From this result, a series of lemmata is derived establishing the informational completeness of natural covariant localization operators of quantum systems, as well as of the Wigner distributions. The results are applied to phase space representations of the Heisenberg, affine, and Galilean groups.