Related papers: Schrodinger's equation derived from the collision-…
We present a new way of deriving classical mechanics from quantum mechanics. A key feature of the method is its compatibility with the standard approach used to derive transition rates between quantum states due to interactions. We apply…
This paper and abstract have been withdrawn.
It is shown that well-known Vlasov equation can be derived by adding "hidden" degrees of freedom and subsequent quantization. The Shrodinger equation obtained in this manner coincides (in x-representation) with the kinetic equation for the…
A derivation of the time-dependent Schr\"odinger equation from the time-independent one is considered. Instead of time, the coordinate of an additional degree of freedom, the clock, is introduced into the original time-independent…
The transition from classical physics to quantum mechanics has been mysterious. Here, we derive the space-independent von Neumann equation for electron spin mathematically from the classical Bloch or Majorana--Bloch equation, which is also…
The derivation of the time dependent Schr\"odinger equation with transversal and longitudinal relaxation, as the quantum mechanical analog of the classical Landau-Lifshitz-Bloch equation, has been described. Starting from the classical…
We illustrate a simple derivation of the Schrodinger equation, which requires only knowledge of the electromagnetic wave equation and the basics of Einstein's special theory of relativity. We do this by extending the wave equation for…
This paper is painfully withdrawn.
We give an exceptionally short derivation of Schroedinger's equation by replacing the idealization of a point particle by a density distribution.
The Schroedinger- and Klein-Gordon equations are directly derived from classical Lagrangians. The only inputs are given by the discreteness of energy (E=hbar.w) and momentum (p=hbar.k), respectively, as well as the assumed existence of a…
An alternative method is proposed for deriving the time dependent Schroedinger equation from the pictures of wave and matrix mechanics. The derivation is of a mixed classical quantum character, since time is treated as a classical variable,…
The Schr\"odinger equation is universally accepted due to its excellent predictions aligning with observed results within its defined conditions. Nevertheless, it does not seem to possess the simplicity of fundamental laws, such as Newton's…
The Schrodinger equation for non-relativistic quantum systems is derived from some classical physics axioms within an ensemble hamiltonian framework. Such an approach enables one to understand the structure of the equation, in particular…
A linear Boltzmann equation with nonautonomous collision operator is rigorously derived in the Boltzmann-Grad limit for the deterministic dynamics of a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions with…
This paper has been withdrawn by the author
A linear Boltzmann equation is derived in the Boltzmann-Grad scaling for the deterministic dynamics of many interacting particles with random initial data. We study a Rayleigh gas where a tagged particle is undergoing hard-sphere collisions…
The self-similar representation for the Schr\"{o}dinger equation is derived.
A derivation is given of the Boltzmann-Vlasov equation beginning from multiple scattering considerations. The motivation for the discussion, which is purely pedagogical in nature, is the current interest in understanding the origins of…
Schrodinger path to the quantum mechanical wave equation was heuristic and guided more by physical intuition than formal deduction. Here we derive the Schrodinger equation for the particle wave function, assuming that it has a meaning of…
Schrodinger's equation for a single particle is proved from the assumption that dynamics can be formulated in a space whose curvature is the electromagnetic force.