Restrictions imposed by a pure quantum state on the results of measuring the momentum of a particle (2407.04537v3)

Abstract: It is shown that quantum mechanics, including the Born rule for calculating the expectation values of observables for a particle in a given pure state and the Schr\"{o}dinger equation, imposes not only statistical restrictions on the results of measuring observables, but also restrictions on the values of observables themselves that are subject to measurement. However, these restrictions are not as strong as follows from Bohm mechanics. In particular, the quantum formalism defines in the configuration space not one, but two fields of the particle momentum. Both fields satisfy the Heisenberg uncertainty relations. And the key role here is played by the fact that one of the contributions to the Bohm `potential' is actually a contribution to the field characterizing the kinetic energy of the particle.