CALCULATIONS AND NON-NEGATIVE DISTRIBUTIONS IN APPLIED MECHANICS

Abstract

Problems with the measurement device's interface with the micro system are still
unsolved. The focus shifted from the device's effect on the system's state at the start of
quantum mechanics to the inverse problem, which is fundamentally more traditional: how
micro-objects affect the macro-system's state. Multiple interconnected links make up
measuring equipment. The first two cascades can be quantum, according to quantum theory
of measurements, but the third and final one must be classical, or, to use modern language, an
analyzer and a detector. Incorporating such a method of measuring devices into the quantum
mechanical framework is the subject of this research. In fact, the measurement process and
measuring devices can and should be linked to test functions in quantum mechanics with
nonnegative distribution functions (QDF in quantum mechanics Kuryshkin-Wodkevich). We
argue that these operations should be associated with the measuring device and explain how it
communicates with the rest of the system. The fact that the Hamiltonians in QDF are not
Hermitian conveys this link, as it turns out. Consequently, the QDF is gradually coming
together as a quantum theory of measurements, after a long time of being portrayed as an
alternate and exotic quantum theory. The significance of this formalization in the context of
quantum measurement theory was recently elaborated in our publications. Within the context
of studying quantum entanglement, the comparisons between wave functions in the examples
of D. Blokhintsev's measuring instruments and auxiliary functions in QDF theory are
encouraging. These areas of research have the potential to greatly advance quantum
cryptography. In this regard, this work ought to serve as a watershed moment in the QDF's
transition to new uses.