Pauli problem and related mathematical problems

We formulate several mathematical modifications of the Pauli problem of recovering the particle state from the results of measuring its coordinates and momenta, including the most abstract statement of the problem for two projection-valued measures. We describe how the Pauli problem reduces to the problem of finding the eigenvectors of certain operators. The performed analysis introduces the problems of modifications of Pauli pairs, and the considered topics and formulated problems require further study.