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Analytical solutions of the Schrodinger equation are obtained for some diatomic molecular potentials with any angular momentum. The energy eigenvalues and wave functions are calculated exactly. The asymptotic form of the equation is also…
Huygens' principle following from the d'Alembert wave equation is not valid in two-dimensional space. A Schrodinger particle of vanishing angular momentum moving freely in two dimensions experiences an attractive force - the quantum…
A diagonal version of the strong reflection principle is introduced, along with fragments of this principle associated to arbitrary forcing classes. The relationships between the resulting principles and related principles, such as the…
The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…
An analytical solution for a quantum wave impedance in a case of piesewise constant potential was derived. It is in fact an analytical depiction of a well-known iterative method of a quantum wave impedance determination. The expression for…
We discuss the requirement of single valuedness and periodicity of eigenfunction of the third component of the operator of angular momentum. This condition, imposed on a non observable, is often used to derive that the eigenvalues of…
General physics approach is applied to analysis of power components in electrical systems under sinusoidal and non-sinusoidal conditions. Physical essence of active, reactive and distorting powers are determinate. It is shown that the all…
The structure of classical electrodynamics based on the variational principle together with causality and space-time homogeneity is analyzed. It is proved that in this case the 4-potentials are defined uniquely. On the other hand, the…
I argue that nonlocal decision of the outcomes at detection excludes any alternative theory to quantum mechanics: Not all that matters for the results of physical experiments is content in space-time, but all that is in space-time is…
We apply a simple decomposition to the energy of a moving particle. Based on this decomposition, we identify the potential and kinetic energies, then use them to give general definitions of momentum and the various kinds of forces exerted…
Using the positive energy theorem, we derive some constraints on static steller models in asymptotically flat spacetimes in a general setting without imposing spherical symmetry. We show that there exist no regular solutions under certain…
We extend the study of the inertial effects on the dynamics of active agents to the case where self-alignment is present. In contrast with the most common models of active particles, we find that self-alignment, which couples the rotational…
This paper deals with the celebrated Euclidean theorem about isosceles triangles, comparing different proofs.
An exact expression for the determinant of the splitting matrix is derived: it allows us to analyze the asympotic behaviour needed to amend the large angles theorem proposed in Ann. Inst. H. Poincar\'e, B-60, 1, 1994. The asymptotic…
The retarded vector potential of a point magnetic dipole with an arbitrary time dependence undergoing accelerated relativistic motions is derived. A novel expression for the angular distribution of the radiated power of an arbitrary moving…
Inertial manifold theory, saddle point property and exponential dichotomy have been treated as different topics in the literature with different proofs. As a common feature, they all have the purpose of `splitting' the space to understand…
We give a new proof of a convex comparison principle for exterior Bernoulli free boundary problems with discontinuous anisotropy.
Unlike a single Carroll particle, a multiparticle Carroll system can move under suitable conditions, as we demonstrate it explicitly for two particles with a momentum-dependent interaction: the center-of-mass remains fixed, however relative…
The typical central limit theorems in high-frequency asymptotics for semimartingales are results on stable convergence to a mixed normal limit with an unknown conditional variance. Estimating this conditional variance usually is a hard…
The present paper deals with autonomous integral equations with infinite delay via dynamical system approach. Existence, local exponential attractivity, and other properties of center manifold are established by means of the…