Related papers: The Physical Origin of Schr\"odinger Equation
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…
Using a new state-dependent, $\lambda$-deformable, linear functional operator, ${\cal Q}_{\psi}^{\lambda}$, which presents a natural $C^{\infty}$ deformation of quantization, we obtain a uniquely selected non--linear, integro--differential…
After the development of a self-consistent quantum formalism nearly a century ago, there ensued a quest to understand the often counterintuitive predictions of the theory. These endeavors invariably begin with the assumption of the "truth"…
In this initial paper in a series, we first discuss why classical motions of small particles should be treated statistically. Then we show that any attempted statistical description of any nonrelativistic classical system inevitably yields…
We expose the Schr\"odinger quantum mechanics with traditional applications to Hydrogen atom. We discuss carefully the experimental and theoretical background for the introduction of the Schr\"odinger, Pauli and Dirac equations, as well as…
Our goal is the discussion of the problem of mathematical interpretation of basic postulates (or `principles') of Quantum Mechanics: transitions to quantum stationary orbits, the wave-particle duality, and the probabilistic interpretation,…
We present in this continuation paper a new axiomatic derivation of the Schr\"odinger equation from three basic postulates. This new derivation sheds some light on the thermodynamic character of the quantum formalism. We also show the…
By a quantum version of the Arnold transformation of classical mechanics, all quantum dynamical systems whose classical equations of motion are non-homogeneous linear second-order ordinary differential equations, including systems with…
The purpose of the paper is to study the foundations of the main axioms of Quantum Mechanics. From a general study of the mathematical properties of the models used in Physics to represent systems, we prove that the states of a system can…
Quantum mechanics is derived from the principle that the universe contain as much variety as possible, in the sense of maximizing the distinctiveness of each subsystem. The quantum state of a microscopic system is defined to correspond to…
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 momentum representation is seldom used in quantum mechanics courses. Some students are thence surprised by the change in viewpoint when, in doing advanced work, they have to use the momentum rather than the coordinate representation. In…
Several fundamental results in physics are derived from the simple starting point of two commuting orthogonal unit vectors. The combination of these unit vectors leads to spherical harmonics and Schwinger's expression of the…
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…
In this paper, we introduce the Schrodinger equation with a general kinetic energy operator. The conservation law is proved and the probability continuity equation is deducted in a general sense. Examples with a Hermitian kinetic energy…
The formalism of quantum mechanics is presented in a way that its interpretation as a classical field theory is emphasized. Two coupled real fields are defined with given equations of motion. Densities and currents associated to the fields…
In this short letter we review Schwinger's formulation of Quantum Mechanics and we argue that the mathematical structure behind Schwinger's "Symbolism of Atomic Measurements" is that of a groupoid. In this framework, both the Hilbert space…
Classical statistical particle mechanics in the configuration space can be represented by a nonlinear Schrodinger equation. Even without assuming the existence of deterministic particle trajectories, the resulting quantum-like statistical…
From the invariance properties of the Schrodinger equation and the isotropy of space we show that a generic (non-relativistic) quantum system is endowed with an ``external'' motion, which can be interpreted as the motion of the centre of…
The widely known but also somewhat esoteric Mach principle envisages a fully relational formulation of physical theories without any reference to a concept of `absolute space'. When applied to classical mechanics, under the guise of an…