Related papers: On the Quantum Mechanics for One Photon
We show that it is possible to represent various descriptions of Quantum Mechanics in geometrical terms. In particular we start with the space of observables and use the momentum map associated with the unitary group to provide an unified…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
In this paper we review a proposed geometrical formulation of quantum mechanics. We argue that this geometrization makes available mathematical methods from classical mechanics to the quantum frame work. We apply this formulation to the…
A classical circularly polarized electromagnetic wave carries angular momentum, and represents the classical limit of a photon, which carries quantized spin. It is shown that a very similar picture of a circularly polarized coherent wave…
We study a motion of quantum particles, whose properties depend on one coordinate so that they can move freely in the perpendicular direction. A rotationally-symmetric Hamiltonian is derived and applied to study a general interface formed…
One of the most surprising consequences of quantum mechanics is the entanglement of two or more distant particles. Although questions regarding fundamental issues of quantum theory still exist, quantum entanglement has started to play…
We present a unified approach to representations of quantum mechanics on noncommutative spaces with general constant commutators of phase-space variables. We find two phases and duality relations among them in arbitrary dimensions.…
This essay is an attempted to address, from a modern perspective, the motion of a particle. Quantum mechanically, motion consists of a series of localizations due to repeated interactions that, taken close to the limit of the continuum,…
An antisymmetric tensor, the photon tensor, is defined for the description of the photon as a massless relativistic particle. The photon can be visualized as an essentially two dimensional rotating object. The quantum mechanical description…
Elementary particles are found in two different situations: (i) bound to metastable states of matter, for which angular momentum is quantized, and (ii) free, for which, due to their high energy-momentum and leaving aside inner a.m. or spin,…
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…
Employing Maxwell's equations as the field theory of the photon, quantum mechanical operators for spin, chirality, helicity, velocity, momentum, energy and position are derived. The photon ``Zitterbewegung'' along helical paths is explored.…
We prove that a single photon with quantum data encoded in its orbital angular momentum can be manipulated with simple optical elements to provide any desired quantum computation. We will show how to build any quantum unitary operator using…
Based on quantum mechanical approach the polarization transport of photons which propagate in a medium with slow varying refractive index is studied. The photon polarizations are separated in opposite directions normal to the ray which is…
There is a unique finite group that lies inside the 2-dimensional unitary group but not in the special unitary group, and maps by the symmetric square to an irreducible subgroup of the 3-dimensional real special orthogonal group. In an…
A review of the photon-number tomography and symplectic tomography as examples of star-product quantization is presented. The classical statistical mechanics is considered within the framework of the tomographic representation.
States of a quantum mechanical system are represented by rays in a complex Hilbert space. The space of rays has, naturally, the structure of a K\"ahler manifold. This leads to a geometrical formulation of the postulates of quantum mechanics…
Quantum mechanics is usually presented starting from a series of postulates about the mathematical framework. In this work we show that those same postulates can be derived by assuming that measurements are discrete interactions: that is,…
Approximation methods for calculating individual particle/ field motions in spacetime at the quantum level of accuracy (a key feature of the Bohm Picture of Quantum Mechanics (BP)), are studied. Modern textbook presentations of Quantum…
We second quantize the Fermi Lagrangian in the Lorenz gauge to obtain a covariant theory of photon quantum mechanics. Number density is real so it is interpreted as position probability density. The Hilbert space is the vector space of…