Related papers: Raising and lowering operators for angular momentu…
The angular wave functions for a hydrogen atom are well known to be spherical harmonics, and are obtained as the solutions of a partial differential equation. However, the differential operator is given by the Casimir operator of the…
In quantum mechanics textbooks the momentum operator is defined in the Cartesian coordinates and rarely the form of the momentum operator in spherical polar coordinates is discussed. Consequently one always generalizes the Cartesian…
In the present paper we construct a properly defined quantum state expressed in terms of elliptic Jacobi theta functions for the self-adjoint observables angular position $\theta$ and the corresponding angular momentum operator $L =…
We extend former results for coherent states on the circle in the literature in two ways. On the one hand, we show that expectation values of fractional powers of momentum operators can be computed exactly analytically by means of Kummer's…
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…
The quantum theory of rotation angles (S. M. Barnett and D. T. Pegg, Phys. Rev. A, 41, 3427-3425 (1990)) is generalised to non-integer values of the orbital angular momentum. This requires the introduction of an additional parameter, the…
Using singlet S states of the helium atom as an example, I describe precise calculation of energy levels in few-electron atoms. In particular, a complete set of effective operators is derived which generates O(m*alpha^6) relativistic and…
Courses on undergraduate quantum mechanics usually focus on solutions of the Schr\"odinger equation for several simple one-dimensional examples. When the notion of a Hilbert space is introduced only academic examples are used, such as the…
We derive the effective angular momentum operator to $1/m^2$ and one-loop order in non-relativistic quantum electrodynamics (NRQED). In both dimensional and three-momentum-cutoff regularization schemes, we obtain the non-relativistic…
The Schr\"odinger equations for the Coulomb and the Harmonic oscillator potentials are solved in the cosmic-string conical space-time. The spherical harmonics with angular deficit are introduced. The algebraic construction of the harmonic…
A revised program for generating the spin-angular coefficients in relativistic atomic structure calculations is presented. When compared with our previous version [G.Gaigalas, S.Fritzsche and I.P.Grant, CPC 139 (2001) 263], the new version…
Our new formulation of the Spherical Collapse Model (SCM-L) takes into account the presence of angular momentum associated with the motion of galaxy groups infalling towards the centre of galaxy clusters. The angular momentum is responsible…
In the frame of the Lindblad theory of open quantum systems, the system of three uncoupled harmonic oscillators with opening operators linear in the coordinates and momenta of the considered system is analyzed. The damping of the angular…
The ladder operators for one dimensional quantum harmonic oscillator were constructed by Schr\"odinger in 1940s. We extend this method to a two dimensional uniform magnetic field and establish the ladder operators which depend on all…
In this paper, quantum mechanics on a circle with finite number of {\alpha}-uniformly distributed points is discussed. The angle operator and translation operator are defined. Using discrete angle representation, two types of discrete…
In this paper, we construct corrections to the raising and lowering (i.e. ladder) operators for a quantum harmonic oscillator subjected to a polynomial type perturbation of any degree and to any order in perturbation theory. We apply our…
The recently established existence of spherical harmonic functions, $Y_\ell^{m}(\theta,\phi)$ for half-odd-integer values of $\ell$ and $m$, allows for the introduction into quantum chemistry of explicit electron spin-coordinates; i.e.…
For a q-deformed harmonic oscillator, we find explicit coordinate representations of the creation and annihilation operators, eigenfunctions, and coherent states (the last being defined as eigenstates of the annihilation operator). We…
On a cubic lattice the zero-momentum meson states have one of 20 possible Lambda^{PC} combinations where Lambda labels the irreducible representation of the octahedral group. Each continuum bottomonium state with specific J^{PC} quantum…
We discuss generic spin squeezing operators (quadratic in angular momentum operators) capable of squeezing out quantum mechanical noise from a system of two-level atoms (spins) in a coherent state. Such systems have been considered by…