Related papers: Accurate S-state helium wave functions in momentum…
The problem of quantum harmonic oscillator with "regular+random" square frequency, subjected to "regular+random external force, is considered in framework of representation of the wave function by complex-valued random process. Average…
On the basis of variational method we study energy levels of pionic helium $(\pi-e-He)$ and kaonic helium $(K-e-He)$ with an electron in ground state and a meson in excited state with principal and orbital quantum numbers $n\sim l+1\sim…
In this brief note we derive and present the formulas necessary to correct measurements of cumulants for detection efficiency. In particular we consider the case where the efficiency may depend on the phase-space, such as transverse…
A different approach has been used to evaluate the momentum imparted by the gravitational waves with spherical wavefronts. It is shown that the results obtained for momentum coincide with those already available in the literature.
By using the Fourier transforms of the general hydrogenic bound state wave functions (as ultraspherical polynomials) one may find expectation values of arbitrary functions of momentum p. In this manner the effect of a reciprocity…
Formulas and expectation values which are need to determine the lowest-order QED corrections ($\sim \alpha^3$) and corresponding recoil (or finite mass) corrections in the two-electron helium-like ions are presented. Other important…
n a recent paper we proposed the expansion of the space of variations in energy calculations by considering the approximate wave function $\psi$ to be a functional of functions $\chi: \psi = \psi[\chi]$ rather than a function. For the…
We report on the observation of phase space modulations in the correlated electron emission after strong field double ionization of helium using laser pulses with a wavelength of 394~nm and an intensity of $3\cdot10^{14}$W/cm$^2$. Those…
Quantum polyhedra constructed from angular momentum operators are the building blocks of space in its quantum description as advocated by Loop Quantum Gravity. Here we extend previous results on the semiclassical properties of quantum…
We use the idea of the symmetry between the spacetime coordinates x^\mu and the energy-momentum p^\mu in quantum theory to construct a momentum space quantum gravity geometry with a metric s_{\mu\nu} and a curvature P^\lambda_{\mu\nu\rho}.…
This paper explains existing results for the application of special functions to phase estimation, which is a fundamental topic in quantum information. We focus on two special functions. One is prolate spheroidal wave function, which…
In quantum mechanics, spatial wavefunctions describe distributions of a particle's position or momentum, but not of angular momentum $j$. In contrast, here we show that a spatial wavefunction, $j_m (\phi,\theta,\chi)=~e^{i m \phi} \delta…
The proper vertex amplitude is derived from the EPRL vertex by restricting to a single gravitational sector in order to achieve the correct semi-classical behaviour. We apply the proper vertex to calculate a cosmological transition…
We use nonstandard analysis to formulate quantum mechanics in hyperfinite-dimensional spaces. Self-adjoint operators on hyperfinite-dimensional spaces have complete eigensets, and bound states and continuum states of a Hamiltonian can thus…
Effective potentials of the relativistic m\alpha^6 order correction for the ground state of the Coulomb two-center problem are calculated. They can be used to evaluate the relativistic contribution of that order to the energies of hydrogen…
We present a new algorithm to calculate exact hypervolumes. Given a set of $d$-dimensional points, it computes the hypervolume of the dominated space. Determining this value is an important subroutine of Multiobjective Evolutionary…
An analytical expression for the relativistic corrections to the energy spectra of particles completely confined in an one-dimensional limited length in real space is given, based upon the wave property of particles, the relativistic…
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…
We discuss correspondence between the predictions of quantum theories for rotation angle formulated in infinite and finite dimensional Hilbert spaces, taking as example, the calculation of matrix elements of phase-angular momentum…
In contrast to wave functions in nonrelativistic quantum mechanics interpreted as probability amplitudes, wave functions in relativistic quantum mechanics have generalized meanings such as charge-density amplitudes, energy-density…