Related papers: Schrodinger's original quantum-mechanical solution…
Contrary to popular belief, the Zeeman effect can be treated exactly in single-electron systems, for arbitrary magnetic field strengths, as long as the term quadratic in the magnetic field can be ignored. These formulas were actually…
We discuss the solutions of the Schroedinger equation for piecewise potentials, given by the harmonic oscillator potential for $\vert x\vert >a$ and an arbitrary function for $\vert x\vert <a$, using elementary methods. The study of this…
We present a simple new way - called Schrodingerisation - to simulate general linear partial differential equations via quantum simulation. Using a simple new transform, referred to as the warped phase transformation, any linear partial…
According to Schroedinger's ideas, classical dynamics of point particles should correspond to the " geometrical optics " limit of a linear wave equation, in the same way as ray optics is the limit of wave optics. It is shown that, using…
We analyze the Schr\"{o}dinger dynamics and the Schr\"{o}dinger function (or the so-called wavefunction) in the following four aspects. (1) The Schr\"{o}dinger equation is reconstructed from scratch in the real field only, without referring…
We generalize Schroedinger's factorization method for Hydrogen from the conventional separation into angular and radial coordinates to a Cartesian-based factorization. Unique to this approach, is the fact that the Hamiltonian is represented…
Elaborating on M. Pavon, J.Math. Phys. 40 (1999), 5565-5577, we develop a simplified version of a variational principle within Nelson stochastic mechanics that produces the von Neumann wave packet reduction after a position measurement.…
Two major deviations from causality in the existing formulations of quantum mechanics, related respectively to quantum chaos and indeterminate wave reduction, are eliminated within the new, universal concept of dynamic complexity. The…
We present a highly accurate method for solving single-active-electron (SAE) atomic eigenset in momentum space. The trouble of Coulomb kernel singularity is bypassed with numerical quadrature, which is simple but effective. The complicated…
Quantum mechanics take the sum of first finite order approximate solutions of time-dependent perturbation to substitute the exact solution. From the point of mathematics, it may be correct only in the convergent region of the time-dependent…
The physical model of a nonrelativistic quantized Schrodinger's electron (SE) is offered. The behaviour of the SE well spread elementary electric charge had been understood by means of two independent and different in a frequency and size…
The Legendre transform expresses dynamics of a classical system through first-order Hamiltonian equations. We consider coherent state transforms with a similar effect in quantum mechanics: they reduce certain quantum Hamiltonians to…
Most authors of textbooks on quantum mechanics either postulate or sketch a short `ad hoc` derivation of Schrodinger's equation. In this work we give a detailed derivation of Schrodinger's equation from the Hamilton-Jacobi equation and the…
Schrodinger's equation predicts something very peculiar about the electron in the Hydrogen atom: its total energy must be equal to zero. Unfortunately, an analysis of a zero-energy wavefunction for the electron in the Hydrogen atom has not…
The method is an extension to negative energies of a spectral integral equation method to solve the Schroedinger equation, developed previously for scattering applications. One important innovation is a re-scaling procedure in order to…
Schr{\"o}dinger noticed in 1952 that a scalar complex wave function can be made real by a gauge transformation. The author showed recently that one real function is also enough to describe matter in the Dirac equation in an arbitrary…
In 1948, Schwinger developed a local Lorentz covariant formulation of relativistic quantum electrodynamics in space-time which is fundamentally inconsistent with any delocalized interpretation of quantum mechanics. An interpretation…
This paper systematically develops the Schr\"odinger formalism that is valid also for gyrotropic media where the material weights $W = \left ( \begin{smallmatrix} \varepsilon & \chi \chi^* & \mu \end{smallmatrix} \right ) \neq \overline{W}$…
A central problem in quantum mechanics involves solving the Electronic Schrodinger Equation for a molecule or material. The Variational Monte Carlo approach to this problem approximates a particular variational objective via sampling, and…
In two respects Ludwig Boltzmann was a pioneer of quantum mechanics. First because in his statistical interpretation of the second law of thermodynamics he introduced the theory of probability into a fundamental law of physics and thus…