The structural form of the Kuryshkin-Wodkiewicz model of quantum measurement was developed in detail for quantum Kepler problem. For more complex objects such quantumstructure is unknown. At the same time, a standard (non-structural) model of quantum measurement proposed by Holevo-Helstrom is suitable for any quantum object. The aim of thiswork is to spread the structural model of quantum measurement to a broader class of quantum objects a model of quantum measurements of optical spectra of atoms and ions with one valence electron. In this work the Kuryshkin-Wodkiewicz model with implementation of Weyl-Kuryshkin quantization rule is applied to the extended quantum Kepler problem of quantum systems with one valence electron, such as alkali metal atoms. The proof of the consistency of the model is based on two Kato theorems about compact perturbations of operators. In the proof process the explicit form of the discrete spectrum of the valence electron for various spectral series was achieved with dependence on the serial parameters of the disturbance spectrum of an isolated object in the process of quantum measurement.
The structural form of the Kuryshkin-Wodkiewicz model of quantum measurement was developed in detail for quantum Kepler problem. For more complex objects such quantumstructure is unknown. At the same time, a standard (non-structural) model of quantum measurement proposed by Holevo-Helstrom is suitable for any quantum object. The aim of thiswork is to spread the structural model of quantum measurement to a broader class of quantum objects a model of quantum measurements of optical spectra of atoms and ions with one valence electron. In this work the Kuryshkin-Wodkiewicz model with implementation of Weyl-Kuryshkin quantization rule is applied to the extended quantum Kepler problem of quantum systems with one valence electron, such as alkali metal atoms. The proof of the consistency of the model is based on two Kato theorems about compact perturbations of operators. In the proof process the explicit form of the discrete spectrum of the valence electron for various spectral series was achieved with dependence on the serial parameters of the disturbance spectrum of an isolated object in the process of quantum measurement.
The constructive form of the Kuryshkin-Wodkiewicz model of quantum measurements was earlier developed in detail for the quantum Kepler problem. For more complex quantum objects, such a construction is unknown. At the same time, the standard (non-constructive) model of Holevo-Helstrom quantum measurements is suitable for any quantum object. In this work, the constructive model of quantum measurements is generalized to a wider class of quantum objects, i.e., the optical spectrum of atoms and ions with one valence electron. The analysis is based on experimental data on the energy ordering of electrons in an atom according to the Klechkovsky-Madelung rule and on the substantiation of a single-particle potential model for describing the energy spectrum of optical electrons in alkali metal atoms. A representation of the perturbation of a single-particle potential in the form of a convolution of the potential of an electron in a hydrogen atom with the Wigner function of a certain effective state of the core in an alkali metal atom representation allows reducing all calculation algorithms for alkali metals to the corresponding algorithms for the hydrogen atom.
This report investigates the flawed foundations of standard quantum theory based on a misunderstanding of the role of measurement. The report is major part of a research programme (UET) based on a new theory of the electromagnetism (EM), centered exclusively on the interaction between electrons. All the previous papers to date in this series have presented a realistic view of the dynamics of two or more electrons as they interact only between themselves. This paper now posits a theory of how this microscopic activity is perceived by human beings in attempting to extract information about atomic systems. The standard theory of quantum mechanics (QM) is constructed on only how the micro-world appears to macro measurements - as such, it cannot offer any view of how the foundations of the world are acting when humans are not observing it (the vast majority of the time) - this has generated almost 100 years of confusion and contradiction at the very heart of physics. All human beings (and all our instruments) are vast collections of electrons, our information about atomic-scale can only be obtained destructively and statistically. This theory now extends the realistic model of digital electrons by adding an explicit measurement model of how our macro instruments interfere with nature's micro-systems when such attempts result in human-scale information. The focus here is on the connection between the micro-world (when left to itself) and our mental models of this sphere of material reality, via the mechanism of atomic measurements. The mathematics of quantum mechanics reflects the eigenvalues of the combined target system plus equipment used for measurement together. Therefore, QM has constructed a theory that inseparably conflates the ontological and epistemological views of nature. This standard approach fails to examine isolated target systems alone. It is metaphysically deficient. This investigation concludes that the Quantum State function (Ψ) is not a representation of physical reality, within a single atom, but a generator function for producing the average statistical results on many atoms of this type. In contrast, the present theory builds on the physical reality of micro-states of single atoms, where (in the case of hydrogen), a single electron executes a series of fixed segments (corresponding to the micro-states) across the atom between a finite number of discrete interactions between the electron and one of the positrons in the nucleus. The set of serial segments form closed trajectories with real temporal periods, contra to Heisenberg’s ‘papal’ decree banning such reality because of his need to measure position and momentum at all times. This is the first paper in the multi-paper series (UET7n), which is dedicated to analyzing, criticizing and replacing existing theories of quantum mechanics.
One of the possible versions of quantum mechanics, known as Kuryshkin-Wodkiewicz quantum mechanics, is considered. In this version, the quantum distribution function is positive, but, as a retribution for this, the von Neumann quantization rule is replaced by a more complicated rule, in which an observed value AA is associated with a pseudodifferential operator O^(A){\hat{O}(A)}. This version is an example of a dissipative quantum system and, therefore, it was expected that the eigenvalues of the Hamiltonian should have imaginary parts. However, the discrete spectrum of the Hamiltonian of a hydrogen-like atom in this theory turned out to be real-valued. In this paper, we propose the following explanation for this paradox. It is traditionally assumed that in some state ψ{\psi} the quantity AA is equal to λ{\lambda} if ψ{\psi} is an eigenfunction of the operator O^(A){\hat{O}(A)}. In this case, the variance O^((A-λ)2)ψ{\hat{O}((A-\lambda)2)\psi} is zero in the standard version of quantum mechanics, but nonzero in Kuryshkins mechanics. Therefore, it is possible to consider such a range of values and states corresponding to them for which the variance O^((A-λ)2){\hat{O}((A-\lambda)2)} is zero. The spectrum of the quadratic pencil O^(A2)-2O^(A)λ+λ2E^{\hat{O}(A2)-2\hat{O}(A)\lambda + \lambda 2 \hat{E}} is studied by the methods of perturbation theory under the assumption of small variance D^(A)=O^(A2)-O^(A)2{\hat{D}(A) = \hat{O}(A2) - \hat{O}(A) 2} of the observable AA. It is shown that in the neighborhood of the real eigenvalue λ{\lambda} of the operator O^(A){\hat{O}(A)}, there are two eigenvalues of the operator pencil, which differ in the first order of perturbation theory by ±i⟨D^⟩{\pm i \sqrt{\langle \hat{D} \rangle}}.
Quantum theory of measurements is an extremely important part of quantum mechanics. Currently perturbations by quantum measurements of observable quantities of atomic systems are rarely taken into account in computing algorithms and calculations. In the previous studies of the authors, constructive model of quantum measurements has been developed and implemented in the form of symbolic and numerical calculations for the hydrogen-like atoms. This work describes a generalization of these results to the alkali metal atoms.
The transfer of quantum information via quantum communication channels necessarily includes the process of quantum measurements of output. If we ignore the full description of the functioning of such channels, and focus only on the procedure of quantum measurements, we should work with the most mathematically rigorous standard Holevo model of quantum measurements. The Kuryshkin-Wodkiewicz quantum mechanics is a constructive version of the standard model, which includes a description of the phase representation of quantum mechanics. The longest living pure states in the dissipative quantum model under study are states with minimal dispersion. The work is devoted to an approximate numerical solution of the problem of finding such states.
The measuring process of an object system and a detector are studied in the von Neumann model and one of its variants, in which the detector consists of a single particle. If the states of the particle after the interaction with the object system are described partly by coherent states, then the particle can play the role of a detector under certain conditions. The mass (or free Hamiltonian) of the detector does not affect the measuring process at all, while the mass of the object system plays an important role. In the von Neumann model, if the mass of the object system is quite large, the position measurement can be considered, and under certain conditions the statistical operator \ensuremath{\rho} tends to just its mixed-state part, i.e., quantum interference disappears. However, when the time after the interaction becomes very large, interference emerges again. On the other hand, if the mass of the object system is small, we can even consider the momentum measurement and show that \ensuremath{\rho} approaches its mixed-state part when the time becomes very large, i.e., \ensuremath{\rho} is equivalent to its mixed-state part. The momentum can also be measured almost completely in the variant model; the operator \ensuremath{\rho} becomes equivalent to its mixed-state part. The different quantum states distinguish the detectors from the object systems.