Analytic solutions for time-dependent Schrödinger equations with linear of nonlinear Hamiltonians

The decomposition method is applied to the time-dependent Schrödinger equation for linear or nonlinear Hamiltonian operators, without linearization, perturbation, or numerical methods, to obtain a rapidly converging analytic solution     

Solitary waves on a curved space-time

A nonlinear partial differential equation is derived which admits plane solitary waves on a conformally flat Riemannian space-time. The metric is determined by the amplitude of these waves. By interpreting these solitary waves as particles we arrive at the following picture: these particles are confined to regions exhibiting singular (very large) amplitudes in an otherwise continuous wavetrain. There is, thus, no distinction between the notion of a particle and that of a wave.     

On bound state solutions for certain nonlinear Schrödinger equations

We show that techniques suitable for studying the bound state problem for the linear Schrödinger equation are also applicable to certain nonlinear generalizations. A sufficient condition for the absence of bound states and a family of lower bounds on the eigenvalues are derived.     

Nonlinear Schrödinger mechanics and the law of gravity

This paper is a study of the consequences that follow from modeling a nonlinear and nonrelativistic quantum theory for gravitating particles. At present there exists no relativistic generalizations that do not sacrifice certain assumptions which are standard in covariant field theories.     

über die Selbstenergie und Ladung eines durch Gravitationswirkungen stabilisierten Teilchens in einem gekrümmten Raum

The problem of the self-energy and the charge of particles is discussed by solvingEinstein's field-equations of general Relativity.

The mass and the charge of a particle are fixed by its radius. If the background is flat the specific chargege/m is an universal constant, if the particle is embedded in a De-Sitter universege/m depends on the particle-radius.

     

On the measure of proper time in general relativity

The theoretical measure of proper time on a moving particle in general relativity is the aggregate of infinitesimal clock readings in successive inertial frames along its space-time path. This raises the question of whether the proper time can be satisfactorily measured by a clock permanently located with the particle. An investigation is made of the likely effects of acceleration, or equivalently of a gravitational field, on atomic, nuclear, and particle clocks. The orders of magnitude of such effects are compared with those of other classical influences such as the Einstein redshift and transverse Doppler effects.     

Embedding of a relativistic charged particle

A charged particle following the Reissner-Weyl vacuum field-distribution shows in its interior a real singularity (the matter-tensor becomes infinite). By embedding the interior submanifoldds ²=g ₁₁·dr ²+g ₀₀·dt ² into a pseudo-Euclidean spaceE ₃:ds ²=dZ ₁ ² +dZ ₂ ² –dZ ₃ ² one finds that the embedded (r, t)-metric looks like a cone with the top liying in theZ ₁,Z ₂ plane. The general formulas of embedding the complete manifold into a pseudo-Euclidean spaceE ₆ are discussed.