Related papers: Wave functions for the regular pentagonal two-dime…
For a spinless quantum particle in a one-dimensional box or an electromagnetic wave in a one-dimensional cavity, the respective Dirichlet and Neumann boundary conditions both lead to non-degenerate wave functions. However, in two spatial…
We show that the spectrum of orbital angular momentum in quantum mechanics consists of two parts when the underlying space has periodic boundaries. While the first part consists of the usual textbook integer quantized values, the second is…
One and two photon wave functions are derived by projecting the quantum state vector onto simultaneous eigenvectors of the number operator and a recently constructed photon position operator [Phys. Rev A 59, 954 (1999)] that couples spin…
We prove the existence of a set of two-scale magnetic Wannier orbitals w_{m,n}(r) on the infinite plane. The quantum numbers of these states are the positions {m,n} of their centers which form a von Neumann lattice. Function w_{00}localized…
We have calculated a discrete spectrum and found an exact analytical solution in the form of Meixner polynomials for the wave function of a thin gravitating shell in the Reissner-Nordstrom geometry. We show that there is no extreme state in…
We present analytic results for all planar two-loop Feynman integrals contributing to five-particle scattering amplitudes with one external massive leg. We express the integrals in terms of a basis of algebraically-independent…
The quantum resonances of classically chaotic n-disk geometries were studied experimentally utilizing thin 2-D microwave geometries. The experiments yield the frequencies and widths of low-lying resonances, which are compared with…
A quaternionic wavefunction consisting of real and scalar functions is found to satisfy the quaternionic momentum eigenvalue equation. Each of these components are found to satisfy a generalized wave equation of the form…
The tunable interaction between stationary quantum bits and propagating modes of light allows for the encoding of quantum information in the state of itinerant photons. This ability fulfills a central requirement for quantum networking,…
We investigate properties of the transmission amplitude of quantum graphs and microwave networks composed of regular polygons such as triangles and squares. We show that for the graphs composed of regular polygons with the edges of the…
Quantum graphs and their experimental counterparts, microwave networks, are ideally suited to study the spectral statistics of chaotic systems. The graph spectrum is obtained from the zeros of a secular determinant derived from energy and…
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…
We report an infinite number of orthonormal wave functions bases for the quantum problem of a free particle in presence of an applied external magnetic field. Each set of orthonormal wave functions (basis) is labeled by an integer $p$,…
A method is proposed to find the wave function of an electron moving infinitely in the field of an arbitrary 1D layer structure with two different homogeneous semi-infinite boundaries. It is shown that in general the problem reduces to…
Quantum phase-space distributions (Wigner functions) for the plane rotator are defined using wave functions expressed in both angle and angular momentum representations, with emphasis on the quantum superposition between the Fourier dual…
In absence of currents and charges the quantized electromagnetic field can be described by wave functions which for each individual wave vector are normalized to one. The resulting formalism involves reducible representations of the…
The wave function in quantum mechanics presents an interesting challenge to our understanding of the physical world. In this paper, I show that the wave function can be understood as four intrinsic relations on physical space. My account…
A pseudo-Riemannian manifold contains an inherent Hamiltonian structure within the symplectic manifold in the cotangent bundle corresponding to the metric. Using this structure, it is possible to define a Hamiltonian, which can be…
We consider transverse propagation of electromagnetic waves through a two-dimensional composite material containing a periodic rectangular array of circular cylinders. Propagation of waves is described by the Helmholtz equation with the…
We generalize the known solution of the Schr\"odinger equation, describing a particle confined to a triangular area, for a triangular graphene quantum dot with armchair-type boundaries. The quantization conditions, wave functions, and the…