Related papers: Critical comments on quantization of the angular m…
Based on the recent construction of a self-adjoint momentum operator for a particle confined in a one-dimensional interval, we extend the construction to arbitrarily shaped regions in any number of dimensions. Different components of the…
Position and momentum observables are considered and their correlation is studied for the simplest quantum system of a free particle moving in one dimension. The algebra and the eigenvalue problem for the correlation observable is presented…
Using heuristic arguments alone, based on the properties of the wavefunctions, we obtain the energy eigenvalues and the corresponding eigenfunctions of the one-dimensional harmonic oscillator. This approach is considerably simpler and is…
A plane, monochromatic electromagnetic wave propagating in free space can have a certain amount of spin angular momentum but cannot possess any orbital angular momentum. Even the spin angular momentum of the plane-wave is difficult to…
We compute the angular momentum of the electromagnetic field on a late time Cauchy surface with an arbitrary constant normal vector relevant for the classical scattering of charged particles. We find a time independent contribution to the…
We argue that quantum mechanics makes sense without such controversial postulates as the wave function collapse, the quantum probability rule and the observable postulate. We only need the existence of a wave function as a representation of…
Intimate though the connection is between orbital angular momentum and intrinsic spin, there are differences between them the two quantities. One of them is the fact that while orbital angular momentum has a wave-mechanics description by…
We discuss the uncertainty relations in quantum mechanics on noncommutative plane. In particular, we show that, for a given state at most one out of three basic nontrivial uncertainty relations can be saturated. We consider also in some…
The eigenvalue problem of the Hamiltonian of an electron confined to a plane and subjected to a perpendicular time-independent magnetic field which is the sum of a homogeneous field and an additional field contributed by a singular flux…
The impact of an anti-unitary symmetry on the spectrum of non-hermitean operators is studied. Wigner's normal form of an anti-unitary operator is shown to account for the spectral properties of non-hermitean, PT-symmetric Hamiltonians. Both…
Differences between vector potentials in different gauges contain no dynamics in both classical and quantum electrodynamics and chromodynamics. Consequently, once gauge invariance is established, results calculated in non-covariant gauges…
A renormalizable theory of gravity is obtained if the dimension-less 4-derivative kinetic term of the graviton, which classically suffers from negative unbounded energy, admits a sensible quantisation. We find that a 4-derivative degree of…
We prove quantitative bounds on the eigenvalues of non-selfadjoint bounded and unbounded operators. We use the perturbation determinant to reduce the problem to one of studying the zeroes of a holomorphic function.
Quantum mechanical scalar particle with polarizability is considered in the presence of the Coulomb field. Separation of variables is performed with the use of Wigner $D$-functions, the radial system of 15 equations is reduced to a single…
The non-individuals interpretation of quantum mechanics is presented with the aim of clarifying it and highflying some of its salient features. Alternative formulations of it are proposed and examined.
We reconsider the generalization of standard quantum mechanics in which the position operators do not commute. We argue that the standard formalism found in the literature leads to theories that do not share the symmetries present in the…
The relativistic angular momentum is introduced as an extension of the non-relativistic analysis of allowed states in the phase space for a quantum particle. The paper shows the conceptual basis of the approach. An interesting feature of…
We examine the deformation quantization of a single particle moving in one dimension (i) in the presence of an infinite potential wall, (ii) confined by an infinite square well, and (iii) bound by a delta function potential energy. In…
Momentum is analyzed as a random variable in stochastic quantum mechanics. Arbitrary potential energy functions are considered. The oscillator is presented as an example.
The need for a mathematically rigorous quantization procedure of singular spaces and incomplete motions is pointed out in connection with quantum cosmology. We put our previous suggestion for such a procedure, based on the theory of induced…