Related papers: Quantum relativistic equation for a probability am…
We construct a relativistic quantum mechanics for a boson. To do this we exploit two component wave functions in Dirac type equations of motion. In our formalism we fix the pathological aspect of particle probability density which appears…
Probabilistic description of results of measurements and its consequences for understanding quantum mechanics are discussed. It is shown that the basic mathematical structure of quantum mechanics like the probability amplitude, Born rule,…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
Probability is an important question in the ontological interpretation of quantum mechanics. It has been discussed in some trajectory interpretations such as Bohmian mechanics and stochastic mechanics. New questions arise when the…
The relational interpretation (or RQM, for Relational Quantum Mechanics) solves the measurement problem by considering an ontology of sparse relative events, or "facts". Facts are realized in interactions between any two physical systems…
In the framework of Lagrangian formulation, some q-deformed physical systems are considered. The q-deformed Legendre transformation is obtained for the free motion of a non-relativistic particle on a quantum line. This is subsequently…
Propagation of gravitational and acoustic plane waves in a flat universe filled with a general relativistic, homogeneous and isotropic, spatially flat continuum is studied. The continuum is described by analogues of nonrelativistic…
The one-dimensional motion of $N$ particles in the field of many incoherent waves is revisited numerically. When the wave complex amplitudes are independent, with a gaussian distribution, the quasilinear approximation is found to always…
The relativistic angular momentum is introduced as an extension of the non-relativistic analysis of allowed states in the phase space for a quantum particle. The paper shows the conceptual basis of the approach. An interesting feature of…
In the limit of large quantum excitations, the classical and quantum probability distributions for a Schr\"odinger equation can be compared by using the corresponding WKBJ solutions whose rapid oscillations are averaged. This result is…
I suppose that quantum objects obey elementary probability theory. I consider a connection of elementary probability theory and complex quantum amplitudes by a matrix calculus. A special case of a discrete pregeometry is an example of this…
We introduce a generalized Lagrangian density - involving a non-Hermitian kinetic term - for a quantum particle with the generalized momentum operator. Upon variation of the Lagrangian, we obtain the corresponding Schr\"odinger equation.…
The action reaction principle is violated by the projection of state in some simple quantum measurements. A formulation of Quantum Mechanics in an extended phase space is proposed in order to restore the action reaction principle. All…
A modification of the canonical quantization procedure for systems with time-dependent second-class constraints is discussed and applied to the quantization of the relativistic particle in a plane wave. The time dependence of constraints…
The equation is considered for a composite scalar particle with polarizabilities in an external quantized electromagnetic plane wave. This equation is reduced to a system of equations for infinite number of interacting oscillators. After…
Using the relativistic quantum Hamilton-Jacobi equation within the framework of the equivalence postulate, and grounding one self on both relativistic and quantum Lagrangians, we construct a Lagrangian of relativistic quantum system in one…
In non-relativistic as well as in special relativistic quantum theory, {\em mass} and {\em charge} are {\em pure numbers} appearing in various (quantum) operators and admit {\em any values}, {\it ie}, values for these quantities are to be…
The use of operator methods of algebraic nature is shown to be a very powerful tool to deal with different forms of relativistic wave equations. The methods provide either exact or approximate solutions for various forms of differential…
A "minimal" generalization of Quantum Mechanics is proposed, where the Lagrangian or the action functional is a mapping from the (classical) states of a system to the Lie algebra of a general compact Lie group, and the wave function takes…
A formula to calculate the quantum fluctuations of energy in small subsystems of a hot and relativistic gas is derived. We find an increase in fluctuations for subsystems of small sizes, but we agrees with the energy fluctuations in the…