Related papers: Relationship between quantum mechanics with and wi…
The appearance of noncommuting spatial coordinates is studied in quantum systems containing a magnetic monopole and under the influence of a radial potential. We derive expressions for the commutators of the coordinates that have been…
We show that in complete agreement with classical mechanics, the dynamics of any quantum mechanical wave packet in a linear gravitational potential involves the gravitational and the inertial mass only as their ratio. In contrast, the…
A model of particle interacting with quantum field is considered. The model includes as particular cases the polaron model and non-relativistic quantum electrodynamics. We show that the field operators obey q-commutation relations with q…
Here we prove that the classical (respectively, quantum) system, consisting of a particle moving in a static electromagnetic field, is canonically (respectively, unitarily) equivalent to a harmonic oscillator perturbed by a spatially…
This is a direct computation of the spectral representation of homogeneous spin-weighted spherical random fields with arbitrary integer spin. It generalises known results from Cosmology for the spin-2 Cosmic Microwave Background…
We present a self-contained formulation of spin-free nonrelativistic quantum mechanics that makes no use of wavefunctions or complex amplitudes of any kind. Quantum states are represented as ensembles of real-valued quantum trajectories,…
We consider a stationary spherically symmetric monopole like solution with a finite energy density in a pure quantum chromodynamics (QCD). The solution can be treated as a static Wu-Yang monopole dressed in time dependent field…
Remarkably we find that for a ring with linear boundary conditions such that the eigenvector and its derivative are continuous, there does not seem to be a way for the well-known de Broglie relation to be gauge invariant. Certain nonlinear…
We analyze the control by electromagnetic fields of quantum systems with infinite dimensional Hilbert space and a discrete spectrum. Based on recent mathematical results, we rigorously show under which conditions such a system can be…
Standard quantum mechanics is viewed as a limit of a cut system with artificially restricted dimension of a Hilbert space. Exact spectrum of cut momentum and coordinate operators is derived and the limiting transition to the infinite…
We consider the quantum mechanics of Calogero models in an oscillator or Coulomb potential on the N-dimensional sphere. Their Hamiltonians are obtained by an appropriate Dunkl deformation of the oscillator/Coulomb system on the sphere and…
We present a theory of quantum oscillations in insulators that are particle-hole symmetric and non-topological but with arbitrary band dispersion, at both zero and non-zero temperature. At temperatures $T$ less than or comparable to the…
Spin is commonly thought to reflect the true quantum nature of microphysics. We show that spin is related to intrinsic and field-like properties of single particles. These properties change continuously in external magnetic fields.…
A general analytic spherically symmetric solution of the Bogomol'nyi equations is found. It depends on two constants and one arbitrary function on radius and contains the Bogomol'nyi-Prasad-Sommerfield and Singleton solutions as particular…
In analogy with conventional quantum mechanics, non-commutative quantum mechanics is formulated as a quantum system on the Hilbert space of Hilbert-Schmidt operators acting on non-commutative configuration space. It is argued that the…
In the present article, we discuss a modification of classical electrodynamics in which ``ordinary'' point charges are absent. The modified equations contain additional terms describing the induced charges and currents. The densities of the…
We discuss the quantum mechanics of particles of arbitrary statistics on an infinite cylinder with and without a magnetic field perpendicular to the surface. In the presence of a magnetic field, the translational symmetry along the cylinder…
Quantum-mechanical wave equation for a particle with spin 1 is investigated in presence of external magnetic field in spaces with non-Euclidean geometry with constant positive curvature. Separation of the variable is performed; differential…
The wave functions of a quantum isotropic harmonic oscillator in N-space modified by barriers at the coordinate hyperplanes can be expressed in terms of certain generalized spherical harmonics. These are associated with a product-type…
A linear quantum harmonic oscillator factors into one dimensional oscillators and can be solved using creation and annihilation operators. We consider a spherical analogue. This analogue does not factor. The two dimensional case is…