Restrictions imposed by the wave function on the results of measurements
of the particle momentum
- URL: http://arxiv.org/abs/2111.06221v3
- Date: Mon, 6 Jun 2022 15:23:09 GMT
- Title: Restrictions imposed by the wave function on the results of measurements
of the particle momentum
- Authors: N. L. Chuprikov
- Abstract summary: It is shown that knowing the wave function implies not only statistical restrictions on the measurement results.
A key role in establishing the physical meaning of these fields is played by the fact that the field of the kinetic energy operator contains two heterogeneous contributions.
- Score: 0.0
- License: http://creativecommons.org/licenses/by-nc-nd/4.0/
- Abstract: Using the example of the quantum dynamics of a particle in a one-dimensional
configuration space (OCS), it is shown that to know the wave function implies
not only statistical restrictions on the measurement results: the integrand in
the standard formula for calculating the average values of (self-adjoint)
operators and the Schr\"{o}dinger equation for the modulus and phase of the
wave function uniquely also define ' fields of operators' as functions of
coordinate and time. A key role in establishing the physical meaning of these
fields is played by the fact that the field of the kinetic energy operator
contains two heterogeneous contributions: the first is determined by the field
of the momentum operator, which is related only to the phase of the wave
function, and the second coincides with the so-called "quantum mechanical
potential", which is related only to the amplitude of the wave function. The
values of these fields at each point of the OCS are considered as the average
values of the corresponding observables for a pair of noninteracting particles
(for a pair of systems of a one-particle ensemble). At each such point, the
first contribution to the field of kinetic energy describes the kinetic energy
of the center of mass of a pair of particles, and the second -- the energy of
their motion relative to the center of mass. The field of the momentum operator
and the field of the kinetic energy operator, taking into account the K\"{o}nig
theorem, uniquely determine in the OCS two fields of particle momentum values
at each point of the OCS. An analogue of the Heisenberg inequality for the
deviations of both momentum fields from the field of the momentum operator is
obtained.
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