Related papers: The two-dimensional hydrogen atom in The momentum …
We discuss the exact polynomial solutions for the two-dimensional hydrogen atom in a constant magnetic field already studied earlier by other authors. In order to provide a suitable meaning for such solutions we compare them with numerical…
We investigate a semiclassical momentum density energy functional for atoms and show that it yields the same value as the well-known Thomas-Fermi functional. In fact, we show an explicit relation between the minimizers of the two…
The two-body t-matrix is calculated directly as function of two vector momenta for different Malfliet-Tjon type potentials. At a few hundred MeV projectile energy the total amplitude is quite a smooth function showing only a strong peak in…
The Lorentz contraction of bound states in field theory is often appealed to in qualitative descriptions of high energy particle collisions. Surprisingly, the contraction has not been demonstrated explicitly even in simple cases such as the…
In this paper we demonstrate how the Legendre transform connects the statements of Noether's theorem in Hamiltonian and Lagrangian mechanics. We give precise definitions of symmetries and conserved quantities in both the Hamiltonian and…
It is shown that the atom-molecule collision problem in the presence of an external electric field can be solved using the total angular momentum representation in the body-fixed coordinated frame, leading to a computationally efficient…
In a two-dimensional approximation, the probability density and current for a photoelectron near the localization of a quantum vortex are theoretically investigated. The wave function in the momentum representation, which we found earlier,…
A new approach to the geometrization of the electron theory is proposed. The particle wave function is represented by a geometric entity, i.e., Clifford number, with the translation rules possessing the structure of Dirac equation for any…
The nonrelativistic hydrogen atom in $D=3-2\epsilon$ dimensions is the reference system for perturbative schemes used in dimensionally regularized nonrelativistic effective field theories to describe hydrogen-like atoms. Solutions to the…
The application of the Legendre transformation to a hyperregular Lagrangian system results in a Hamiltonian vector field generated by a Hamiltonian defined on the phase space of the mechanical system. The Legendre transformation in its…
A further argument is provided in the discussion on the correct form of the bound-state momentum wave function of the quasi-one-dimensional hydrogen atom; namely, considering its behavior at the large quantum indices, it is reconfirmed that…
The question posed in the title is answered in terms of a simple pictorial argument that is manifestly symmetric between the two functions that are Legendre transform of each other.
Orbital angular momentum eigenfunctions are readily understood in terms of spherical harmonic wavefunctions. However, the quantum mechanical phenomenon of spin is often said to be mysterious and hard to visualize, with no classical…
The constraints imposed on hydrodynamics by the structure of gauge and gravitational anomalies are studied in two dimensions. By explicit integration of the consistent gravitational anomaly, we derive the equilibrium partition function at…
Attosecond chronoscopy typically utilises interfering two-photon transitions to access the phase information. Simulating these two-photon transitions is challenging due to the continuum-continuum transition term. The hydrogenic…
A novel realization of the classical SU(2) algebra is introduced for the Dirac relativistic hydrogen atom defining a set of operators that, besides, allow the factorization of the problem. An extra phase is needed as a new variable in order…
We develop representations for bicomplex-valued functions in Hardy classes that generalize the complex holomorphic Hardy spaces. Using these representations, we show these functions have boundary values in the sense of distributions that…
Expansions over Legendre functions are suggested as a model-independent way of compact presentation of modern precise and high-statistics data for two-hadron reactions. Some properties of the expansions are described.
A simple, and elegant geometrical representation is developed to describe the concept of coherence and squeezing for angular momentum operators. Angular momentum squeezed states were obtained by applying Bogoliubov transformation on the…
The gauge variance of wave functionals for a gauge theory quantized in the momentum (curvature) representation is described. It is shown that a gauge transformation gives rise to a cocycle, which for theories in two space-time dimensions is…