# Quantum corrections to the classical path equations: Multitrajectory and Hermite corrections

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The ground-state wave function and the energy term of a relativistic electron moving in the field of two fixed Coulomb centers are calculated analytically by the LCAO method. The resulting analytic formula is used to calculate the critical internuclear distance at which the energy term crosses...

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Hierarchies of nonlinear SchrÃ¶dinger equations were investigated for multiparticle systems, satisfying the separation property, i.e., where product wave functions evolve by the separate evolution of each factor. Such a hierarchy defines a nonlinear derivation on tensor products of the...

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Exact solutions are found for the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to...

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Apparently, the energy levels merge and disappear in many PT symmetric models. This interpretation is incorrect: In square-well model we demonstrate how the doublets of states in question continue to exist at complex conjugate energies in the strongly nonHermitian regime.

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Focuses on travelling-wave solutions to reaction-diffusion problems which was initiated by Fisher in his work on the Fisher equation. Establishment of the existence and uniqueness of travelling-wave solutions for wave speeds greater than a certain threshold; Formulation of physical problems as...