arXiv subjects

N. L. Chuprikov

Publications and source records attributed to N. L. Chuprikov.

At least 19 recordsLinked to original sources

arXiv2026

The Klein-Gordon-Fock theory as a one-particle relativistic quantum mechanics

The Klein-Gordon-Fock (KGF) theory with the vector potential is presented as a one particle relativistic quantum mechanics (QM). First, the KGF equation is written in a Hamiltonian form, in spinor space; unlike the Feshbach-Villars approach, the Hamiltonian here is strictly Hermitian. Then this equation is rewritten for a one-component wave function. Expressions for the Hamiltonian and other observables' operators acting in the space of one-component wave functions are presented. The nonrelativistic and ultrarelativistic limits of these expressions are considered. A general solution to the KGF equation describing a free particle is presented.

quant-ph↗

arXiv2026

Dirac theory as a one-particle relativistic quantum mechanics in the space of unit two-component spinors

Using the example of a Dirac particle in external static fields, Dirac theory is reformulated as a one-particle quantum theory in the space of normalized two-component spinors. In this formulation, the Dirac operator ``splits'' into two two-component operators: one is bounded from below (in the nonrelativistic limit, it coincides with the Pauli operator), and the other is bounded from above. The first describes the Dirac particle, and the second can be ignored for sufficiently weak external fields. Unlike approaches based on the Foldy-Wouthuysen transformation, the ``splitting'' procedure in our approach is the same for the vector and scalar potentials. It is reduced to solving a second-order algebraic equation for the searched-for operators. A general solution to the free equation for a two-component normalized spinor is presented. Exact analytical expressions are obtained for the two-component analogs of the other Dirac operators, which are then presented in the nonrelativistic and ultrarelativistic limits.

physics.gen-ph↗

arXiv2026

Two gaps in the axiomatics of quantum mechanics

This paper identifies and fixes two gaps in the axiomatics of modern quantum mechanics. The first arises from the unjustified application of the superposition principle in modern quantum scattering theory. The second arises from the incompleteness of the Born interpretation of the wave function.

quant-ph↗

arXiv2026

The deterministic dynamics of a single-particle quantum ensemble is equivalent to the stochastic one due to the indistinguishability of quantum particles

It is shown that the wave function describing the pure state of a single-particle quantum ensemble, in addition to statistical restrictions, imposes restrictions on the particle momentum at points in the configuration space $\mathbb{R}^3$: at time $t$, each point $\mathbf{r}$ is a ``meeting'' point of two (non-interacting) particles of the ensemble with momenta $\mathbf{p}_1(\mathbf{r},t)$ and $\mathbf{p}_2(\mathbf{r},t)$. Their peculiarity is that the velocities $\mathbf{p}_1(\mathbf{r},t)/m$ and $\mathbf{p}_2(\mathbf{r},t)/m$ coincide with the velocities $\mathbf{b}(\mathbf{r},t)$ and $\mathbf{b}_*(\mathbf{r},t)$, which are introduced in Nelson's stochastic approach as key characteristics of frictionless Brownian particle motion. This means that the instantaneous dynamics of a pair of non-interacting quantum particles of an ensemble at point $\mathbf{r}$ at time $t$, due to their fundamental indistinguishability, is equivalent to the collision of two classical Brownian particles. And since this is true at all times for all points in $\mathbb{R}^3$, the unitary deterministic dynamics of a single-particle quantum ensemble is equivalent to a stochastic process.

quant-ph↗

arXiv2026

Asymptotes of non-stationary solutions of the Schrödinger equation for a particle interacting with a one-dimensional $δ$-potential

It is shown that non-stationary solutions of the Schrödinger equation, which describes the quantum dynamics of a particle in the field of a one-dimensional delta potential (1DDP), are divided into two classes: some define pure states that have no free dynamics as $t\to\mp\infty$; others define states with asymptotically free dynamics but represent mixed states in whose space the asymptotic superselection rule holds. That is, according to the Schrödinger equation, {\it pure scattering} states predicted by the conventional model of this scattering process do not exist. On mixed scattering states, the Hamiltonian with 1DDP is defined only in superselection sectors. The scattering process with one-sided incidence of a particle on 1DDP represents a decoherence process in a closed system.

physics.gen-ph↗

arXiv2023

A variational principle, wave-particle duality, and the Schrödinger equation

A principle is proposed according to which the dynamics of a quantum particle in a one-dimensional configuration space (OCS) is determined by a variational problem for two functionals: one is based on the mean value of the Hamilton operator, while the second one is based on the mean value of the total energy of the particle, which is determined through the phase of the wave function with help of the generalized Planck-Einstein relation. The first functional contains information about the corpuscular properties of a quantum particle, and the second one comprises its wave properties. The true dynamics is described by a wave function for which the variations of these two functionals are equal. This variational principle, which can also be viewed as a mathematical formulation of wave-particle duality, leads to the Schrödinger equation.

quant-ph↗

arXiv2021

New about the wave function,"Einstein's boxes'' and scattering a particle on a one-dimensional $δ$-potential

The connection between the problem of scattering a particle on a one-dimensional $δ$-potential with the "Einstein's boxes" thought experiment is shown. In both cases, the validity of the superposition principle is limited by Einstein's 'separation principle'. It is also shown that the generally accepted point of view, according to which "To know the quantum mechanical state of a system implies, in general, only statistical restrictions on the results of measurements", is fundamentally wrong. First, even the square of the modulus of the wave function imposes more than just statistical restrictions. Second, the phase of the wave function also has a physical meaning -- it sets the field of pulses of the ensemble. That is, quantum mechanics not only does not prohibit the simultaneous measurement of the coordinate and momentum of a particle, but also predicts the value of the momentum at that spatial point where the particle will (accidentally) be detected.

physics.gen-ph↗

arXiv2019

Scattering of TE- and TM-polarized wave packets on a dielectric layer: true and false group-delay times

We consider an oblique incidence on a uniform dielectric layer of the plane monochromatic TE- and TM-waves, as well as TE- and TM-polarized wave packets consisting of waves with the same angle of incidence. For each polarization the stationary model is presented, which allows one to uniquely restore the dynamics of the transmitted and reflected components of the incident wave packet at all stages of scattering. On this basis we introduce the concepts of ``true group-delay time"\/ and ``false group-delay time"\/ (the corresponding quantities for transmission and reflection are the same). The former is defined as the difference of two instants in the evolution of the same wave packet, one of which cannot be measured directly. Conversely, the latter is defined as the difference of two instants in the evolution of different wave packets, both can be measured directly. The false group-delay time does not in itself have a physical sense, but plays a key role for an indirect measurement of the true group-delay times of both polarizations.

physics.optics↗

arXiv2016

Revising the applicability of the Stone-von Neumann theorem to scattering a quantum particle on a one-dimensional potential barrier

It is shown that the Stone-von Neumann theorem is inapplicable to scattering a quantum nonrelativistic particle on a one-dimensional "short-range" potential barrier, since the unboundedness of the position operator plays here a crucial role. The Shcrödinger representation associated with this process is reducible: long before and long after the scattering event the space of its asymptotes represents the direct sum of the subspaces of left and right asymptotes. There is a dichotomous-context-induced superselection rule (SSR), in which the role of a superselection operator is played by the Pauli matrix $σ_3$ and the role of superselection (coherent) sectors is played by the above subspaces. By the SSR any superposition of states from different coherent sectors is a mixed state, and splitting the incident wave packet into the transmitted and reflected parts is nothing but a conversion of a pure state into a mixed one. The average values of any observable can be defined only for the transmission and reflection subprocesses. The former evolves within a single coherent sector of the Hilbert space, in the momentum representation; while the latter evolves within a single coherent sector of this space, in the coordinate representation.

physics.gen-ph↗

arXiv2015

The stationary Dirac equation as a generalized Pauli equation for two quasiparticles

By analyzing the Dirac equation with static electric and magnetic fields it is shown that Dirac's theory is nothing but a generalized one-particle quantum theory compatible with the special theory of relativity. This equation describes a {\it quantum} dynamics of a {\it single} relativistic fermion, and its solution is reduced to solution of the generalized Pauli equation for two quasiparticles which move in the Euclidean space with their effective masses holding information about the Lorentzian symmetry of the four-dimensional space-time. We reveal the correspondence between the Dirac bispinor and Pauli spinor (two-component wave function), and show that all four components of the Dirac bispinor correspond to a fermion (or all of them correspond to its antiparticle). Mixing the particle and antiparticle states is prohibited. On this basis we discuss the paradoxical phenomena of Zitterbewegung and the Klein tunneling.

physics.gen-ph↗

arXiv2013

Scattering a quantum particle on the potential step: Characteristic times for transmission and reflection

We present a new model of scattering a quantum particle on the potential step, which reconstructs the prehistory of the subensembles of transmitted and reflected particles by their final states. Unlike the conventional one this model predicts the existence of a transitional spatial region behind the potential step where the probability to find reflected particles is nonzero and the average velocity of transmitted particles monotonously varies between asymptotic values. For both subprocesses we define the dwell and asymptotic group times.

quant-ph↗

arXiv2013

On the generalized Hartman effect and transmission time for a particle tunneling through two identical rectangular potential barriers

We develop a new quantum-mechanical approach to scattering a particle on a one-dimensional (1D) system of two identical rectangular potential barriers, which implies modelling the dynamics of its subprocesses -- transmission and reflection -- at all stages of scattering. On its basis we define, for each subprocess, the dwell time as well as the local (exact) and asymptotic (extrapolated) group times. Our concept of the asymptotic transmission group time confirms the validity of the Wigner phase time in the opaque limit, as well as the existence of the usual and generalized Hartman effects predicted on its basis. On the energy scale, this concept is valid everywhere in the high energy region as well as in the low energy region, excepting resonance points and their neighborhoods. On the contrary, the Buttiker dwell time is valid, as the transmission time, just only at the resonance points. Our concept of the transmission dwell time predicts monotonous growth of the tunneling time when the distance between the opaque barriers increases. By our approach only this time scale yields the true time spent, on average, by transmitted particles in the region occupied by the system. We explain why the asymptotic and local transmission group times cannot play this role and why the concept of {\it transmission group} velocity lies beyond the scope of special relativity. And else, all the transmission times admit only indirect measurements. Hence the unambiguous interpretation of all tunneling-time experiments is impossible when the transmission dynamics at all stages of scattering is unknown.

quant-ph↗

arXiv2011

Two-slit Experiment And Wave-Particle Duality

On the basis of an alternative approach to micro-cat states (Found. of Phys., 41, No. 9, p.1502 (2011)) we develop a new model of the two-slit experiment. It explains both this particular experiment and how the wave properties of any ensemble of single quantum particles emerge from their corpuscular ones. The key role in this explanation is played by the indistinguishability of identical quantum particles.

quant-ph↗

arXiv2011

From a 1D completed scattering and double slit diffraction to the quantum-classical problem for isolated systems

By probability theory the probability space to underlie the set of statistical data described by the squared modulus of a coherent superposition of microscopically distinct (sub)states (CSMDS) is non-Kolmogorovian and, thus, such data are mutually incompatible. For us this fact means that the squared modulus of a CSMDS cannot be unambiguously interpreted as the probability density and quantum mechanics itself, with its current approach to CSMDSs, does not allow a correct statistical interpretation. By the example of a 1D completed scattering and double slit diffraction we develop a new quantum-mechanical approach to CSMDSs, which requires the decomposition of the non-Kolmogorovian probability space associated with the squared modulus of a CSMDS into the sum of Kolmogorovian ones. We adapt to CSMDSs the presented by Khrennikov ({\it Found. of Phys., 35, No. 10, p.1655 (2005)}) concept of real contexts (complexes of physical conditions) to determine uniquely the properties of quantum ensembles. Namely we treat the context to create a time-dependent CSMDS as a complex one consisting of elementary (sub)contexts to create alternative subprocesses. For example, in the two-slit experiment each slit generates its own elementary context and corresponding subprocess. We show that quantum mechanics, with a new approach to CSMDSs, allows a correct statistical interpretation and becomes compatible with classical physics.

quant-ph↗

arXiv2010

From a 1D completed scattering and double slit diffraction to the quantum-classical problem: A new approach

We present a new approach to the quantum-classical problem, which treats it as the problem of modelling the quantum phenomenon described by a coherent superposition of microscopically distinct substates (CSMDS) as a compound one consisting of alternative subprocesses creating unremovable contexts for each other, or as that of reducing a non-Kolmogorovian quantum probability space to underlie a CSMDS to the sum of Kolmogorovian ones. We develop such models for a 1D completed scattering and double slit diffraction. The quantum-classical problem disappears when, in quantum theory with its integral superposition principle, CSMDSs obey the "either-or" rule to guide alternative random events. There is no observable which could be associated with the whole ensemble of statistical data described by a CSMDS, because such data are incompatible -- in the case of a CSMDS, any observable splits into noncommuting observables associated with the substates. To calculate the average value of any observable as well as to introduce characteristic times is meaningful only for the substates of a CSMDS. Ignoring this feature in the conventional description of CSMDSs just leads to paradoxical results (e.g., to the Hartman effect and passing a particle through two slits in the screen simultaneously).

quant-ph↗

arXiv2009

A new mathematical model of tunnelling and the Hartman effect puzzle

In this paper we develop and refine our recent model of a one-dimensional completed scattering, which gives an individual description of the transmission and reflection subprocesses at all stages of scattering. We show that the group, dwell and Larmor characteristic times, introduced in this model for the subprocesses, are in a full agreement with special relativity and allow us to solve the Hartman effect puzzle.

quant-ph↗

arXiv2007

Quantum mechanics as a macrorealistic theory

As contrasted with physicists to idolize Bell's theorem and quantum nonlocality, we argue that quantum mechanics (QM), in reality, respects the principles of a macroscopic realism (PMRs). The current QM to tell us that "... the state of a system can be instantaneously changed by a distant measurement >..." cannot be treated as a physical theory. Its key statements - that the EPR-Bell experiments to violate Bell's inequality verify nonlocality, and nonlocal correlations respect special relativity - are false. Both the EPR-Bell experiments and theorems to support the "non-signalling principle" are based on the implicit assumption that all quantum postulates and, in particular, Born's averaging rule are fully applicable to Cat states. However, this is not the case. Introducing observables (e.g., correlations) for Cat states violates the correspondence principle. Pure (macro- and micro-)Cat states must be governed both by the PMRs and superposition principle. Our (macrorealistic) model of a one-dimensional completed scattering shows how these principles coexist with each other, in the case of a one-electron micro-Cat state.

quant-ph↗

arXiv2007

Quantum mechanics and Leggett's principles of macroscopic realism

On the basis of our recent model of a one-dimensional (1D) completed scattering we argue that Leggett's principles of macroscopic realism must and can be extended onto the level of single electrons and atoms. These principles need three quite feasible innovations in quantum mechanics (QM): (1) at the conceptual level, QM must treat a pure time-dependent one-particle state to involve two or more macroscopically distinct alternatives for a particle as a pure {\it combined} one - the intermediate link between a pure {\it elementary} state (indecomposable into macroscopically distinct parts) and statistical mixture; (2) at the mathematical level, QM must provide the presentation of the pure time-dependent combined state as a coherent superposition of macroscopically distinct elementary states (MDESs); (3) at the experimental level, QM must provide for such states two types of measurements - those for observing the interference pattern resulting from the joint action of MDESs, and non-demolishing 'which-way' measurements for scanning the individual properties of MDESs.

quant-ph↗