Related papers: Schroedingers equation with gauge coupling derived…
In this article, the following results are obtained: the process of a randomly wandering particle having a size and a continuous trajectory of motion is considered; (b) based on the study of this probabilistic process, a derivation of the…
A previous derivation of the single-particle Schr\"odinger equation from statistical assumptions is generalized to an arbitrary number $N$ of particles moving in three-dimensional space. Spin and gauge fields are also taken into account. It…
The Schr\"odinger-like equations for the marginal and conditional probability amplitudes resulting from the exact factorization of the wavefunction of a two-component system are derived in a form that is invariant to gauge and coordinate…
We discuss the functional Schroedinger picture for fermions in external fields for both stationary and time-dependent problems. We give formal results for the ground state and the solution of the time-dependent Schroedinger equation for QED…
Using classical statistics, Schrodinger equation in quantum mechanics is derived from complex space model. Phase-space probability amplitude, that can be defined on classical point of view, has connections to probability amplitude in…
We propose a nonlinear modification of the Schr\"{o}dinger equation that possesses the main properties of this equation such as the Galilean invariance, the weak separability of composite systems, and the homogeneity in the wave function.…
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,…
Grid-based discretizations of the time dependent Schr\"odinger equation coupled to an external magnetic field are converted to manifest gauge invariant discretizations. This is done using generalizations of ideas used in classical lattice…
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…
The local phase-invariance of the momentum-space Schr\"odinger equation for free-particle has been used to construct quantum kinematics that describes a motion of the particle in external U(1) background gauge field. The gauge structure…
In this paper, we reformulate the Schrodinger equation in gauge-theoretic terms. Starting from the Madelung representation, we rewrite the conserved probability-current using gauge fields, namely a one-form gauge field in the…
Using the Wilson formulation of lattice gauge theories, a gauge invariant grid discretization of a one-particle Hamiltonian in the presence of an external electromagnetic field is proposed. This Hamiltonian is compared both with that…
We study a non-linear Schroedinger equation with a Hartree-type nonlinearity and a localized random time-dependent external potential. Sharp dispersive estimates for the linear Schroedinger equation with a random time-dependent potential…
We give an exceptionally short derivation of Schroedinger's equation by replacing the idealization of a point particle by a density distribution.
A Schr\"odinger type equation for a mathematical probability amplitude {\psi}(x,t), is derived from the generalized phase space Liouville equation valid for the motion of a microscopic particle, with mass M, moving in a potential V(x). The…
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.
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…
It is well-known that the coordinate as a continuous variable, consisting of a set of all points between 0 and $L$ contradicts the observability of measurement. In other words there might exist a fundamental length in nature, such as the…
This work studies in detail the possibility of defining a one-to-one mapping from charge densities as obtained by the time-dependent Schr\"odinger equation to external potentials. Such a mapping is provided by the Runge-Gross theorem and…
The consistency of the concept of quantum (quasi)particles possessing effective mass which is both position- and excitation-dependent is analyzed via simplified models. It is shown that the system may be stable even when the effective mass…