Related papers: Is the Wavefunction Already an Object on Space?
Within the class of ontological interpretations of quantum theory where a physical system comprises a particle and a field (wavefunction) guiding it, an empty wave is a segment of the wavefunction not containing the particle. We examine the…
We present an alternative formulation of quantum mechanical angular momentum, based on spatial wavefunctions that depend on the Euler angles $\phi, \theta, \chi$, and have an additional internal projection $n$. The wavefunctions are Wigner…
Path integral formulation of quantum mechanics defines the wavefunction associated with a particle as a sum of phase-factors, which are periodic functions of classical action. In the present article, this periodicity is shown to impart the…
The notion of quantum embedding is considered for two classes of examples: quantum coadjoint orbits in Lie coalgebras and quantum symplectic leaves in spaces with non-Lie permutation relations. A method for constructing irreducible…
The paper addresses the debate about the empirical status of particles versus wave functions in Bohmian quantum mechanics. It thereby clarifies questions and misconceptions about the role of the particles in the measurement process, the…
The space of Gaussian measures on a Euclidean space is geodesically convex in the $L^2$-Wasserstein space. This space is a finite dimensional manifold since Gaussian measures are parameterized by means and covariance matrices. By…
We review the conceptual problems in quantum mechanics on a fundamental level. It is shown that the proposed model of extended electrons and a clear understanding of rotations in three dimensional space solve a large part of these problems,…
Physical geometry studies mutual disposition of geometrical objects and points in space, or space-time, which is described by the distance function d, or by the world function \sigma =d^{2}/2. One suggests a new general method of the…
We present a new geometry of spacetime where events may be positive dimensional. This geometry is obtained by applying the identity of indiscernibles, which is a fundamental principle of quantum statistics, to time. Quantum nonlocality…
At a fundamental level the notion of particle (quantum) comes from quantum field theory. From this point of view we estimate corrections to the free particle wave function due to minimum-length deformed quantum mechanics to the first order…
To get out of logical deadlock in interpreting gedanken experiments like Schrodinger cat, actual meaning of a wave function, or a state, in the case of complex two-dimensional Hilbert space, is shown to represent transformations executing…
Since the 5D canonical metric embeds all 4D vacuum solutions of Einstein's equations, I review its application to the cosmological 'constant', quantized particles, deBroglie waves, scalar fields and wave-particle duality. There are several…
We formulate quantum mechanics in spacetimes with real-order fractional geometry and more general factorizable measures. In spacetimes where coordinates and momenta span the whole real line, Heisenberg's principle is proven and the…
Quantum mechanics is often developed in the position representation, but this is not necessary, and one can perform calculations in a representation-independent fashion, even for wavefunctions. In this work, we illustrate how one can…
In this paper I address the most common objections to the claim that Schrodinger was right in 1926: the wavefunction provides the correct, and complete, description of atomic phenomena. I suggest that the line of droplets in the Wilson…
The overwhelming majority of scientists still takes it for granted that classical mechanics (ClM) is nothing but a limiting case of quantum mechanics (QM). Although some physicists restrict this belief to a generalized QM as represented, e.…
We present a quaternion wavefunction formulation that reduces the incompressible Euler equations to a single nonlinear Schr\"odinger-type equation with a holomorphic constraint, revealing hidden geometric structure connecting quantum and…
Quantum particles confined to surfaces in higher dimensional spaces are acted upon by forces that exist only as a result of the surface geometry and the quantum mechanical nature of the system. The dynamics are particularly rich when…
We re-use some original ideas of de~Broglie, Schr\"odiger, Dirac and Feynman to revise the ensemble interpretation of wave function in quantum mechanics. To this end we introduce coherence (auto-concordance) of ensembles of quantum…
Euclidean geometry does not characterize dynamic electronic orbitals satisfactorily for even a single electron in a hydrogen atom is a formidable mathematical task with the Schrodinger equation. Here the author puts forward a new spacetime…