Related papers: Wave equations for determining energy-level gaps o…
Schroedinger's equation gave early quantum theory a visual language that looked like physics again: a wave evolving by a linear differential equation. This essay argues that the same success also seeded a recurring impulse to keep quantum…
We propose a definition of wavefunction "branchings": quantum superpositions which can't be feasibly distinguished from the corresponding mixed state, even under time evolution. Our definition is largely independent of interpretations,…
We revisit the treatment of identical particles in quantum mechanics. Two kinds of solutions of Schr\"{o}dinger equation are found and analyzed. First, the known symmetrized and antisymmetrized eigenfunctions. We examine how the very…
Time-dependent quantum mechanics provides an intuitive picture of particle propagation in external fields. Semiclassical methods link the classical trajectories of particles with their quantum mechanical propagation. Many analytical results…
For any kind of wave phenomenon one can find ways to derive the respective dispersion relation from experimental observations and measurements. This dispersion relation determines the structure of the wave equation and thus characterizes…
The wave-particle duality dates back to Einstein's explanation of the photoelectric effect through quanta of light and de Broglie's hypothesis of matter waves. Quantum mechanics uses an abstract description for the behavior of physical…
The quantum mechanical two-body problem with a central interaction on the sphere ${\bf S}^{n}$ is considered. Using recent results in representation theory an ordinary differential equation for some energy levels is found. For several…
A new nonlinear Schroedinger equation is obtained explicitly from the fractal Brownian motion of a massive particle with a complex-valued diffusion constant. Real-valued energy (momentum) plane wave and soliton solutions are found in the…
We investigate the meaning of the wave function by analyzing the mass and charge density distributions of a quantum system. According to protective measurement, a charged quantum system has mass and charge density distributing in space,…
A non perturbative numerical method for determining the discrete spectra is deduced from the classical analogue of the Schrodinger's equation. The energy eigenvalues coincide with the bifurcation parameters for the classical orbits.
Semiclassical (stochastic) wave equations are proposed for the coupled dynamics of atomic quantum states and semiclassical radiation field. All relevant predictions of standard unitary quantum dynamics are exactly reproducible in the…
Bohmian mechanics and the Ghirardi-Rimini-Weber theory provide opposite resolutions of the quantum measurement problem: the former postulates additional variables (the particle positions) besides the wave function, whereas the latter…
The Schrodinger equation based on the de Broglie wave is the most fundamental equation of the quantum mechanics. There can be no doubt about it's prediction validity. However, the probabilistic interpretation on the quantum mechanics has…
It is shown that a wave mechanical quantum theory can be derived from relativistic classical electrodynamics, as a feature of the magnetic interaction of Dirac particles modeled as relativistically circulating point charges. The magnetic…
Our goal in this paper is to initiate the rigorous investigation of wave turbulence and derivation of wave kinetic equations (WKE) for water waves models. This problem has received intense attention in recent years in the context of…
An alternative description of quantum scattering processes rests on inhomogeneous terms amended to the Schroedinger equation. We detail the structure of sources that give rise to multipole scattering waves of definite angular momentum, and…
The functional Schr\"odinger equation in curved space-time is derived from the manifestly covariant precanonical Schr\"odinger equation. The Schr\"odinger wave functional is expressed as the trace of the multidimensional product integral of…
We present a phase space formulation of quantum mechanics in the Schr\"odinger representation and derive the associated Weyl pseudo-differential calculus. We prove that the resulting theory is unitarily equivalent to the standard…
Quantum theory has been remarkably successful in providing an understanding of physical systems at foundational scales. Solving the Schr\"odinger equation provides full knowledge of all dynamical quantities of the physical system. However…
An analysis of the analytical solution of the Schr\"{o}dinger equation (which is a second order differential equation) for $H_2^+$ shows that the second linear independent solution of this equation is a square integrable function and…