I've found the wave-packet picture quite useful as I work my way through the very basics of quantum mechanics. But I'm having trouble finding a wave-mechanical picture of operators. For example, at least in terms of a free particle, using the wave mechanics treatment (as opposed to the matrix mechanics treatment) I think I can very roughly picture: pure states or eigenstates/vectors, following the form eiθ (at least for momentum states) as helical sine waves or phase waves in the complex plane eigenvalues as the amplitudes, moduli or radii of those phase waves in the complex plane wave functions as wave packets or group waves comprised of the interfering component phase waves probabilities as vectors along the real axis of the cross-section of the wave packet in the complex plane But I'm having trouble picturing an operator in this context. Is it possible to picture it at all? My best guess is that it would be a subset of the overall wave packet, and so in some sense a wave packet in its own right, but not sure. Any help would be greatly appreciated.