Momentum-space partial-wave Coulomb functionsAn algorithm to calculate non-relativistic partial-wave Coulomb functions in momentum space is presented. The arguments are the Sommerfeld parameter 畏, the angular momentum l, the asymptotic momentum q and the 'running' momentum p, where both momenta are...
This is particularly the case for plane wave basis sets, where the operations can be performed partly in real space (potential energy) and partly in momentum space (kinetic energy). It is thus not surprising that the conjugate gradient and Car–Parrinello methods are mainly associated with ...
This basis, obtained from the eigenfunctions of the Hamil- tonian (4), consists of a two-dimensional (2D) harmonic oscillator (HO) function φnm in the transverse direction and a modified Jacobi polynomial χl in the longitudinal direction. The transverse basis function in the momentum space ...
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In Matter-Wave: For example, a non-relativistic approximation for an electron wave is given by Where, E is the kinetic energy of the particle m is the mass of the particle p is the momentum of the particle ħ is the reduced Planck’s constant ...
2e–g). However, while the surface streaming-flows are a clear visual marker of the wavefield and direction of rotation, they represent only a higher-order contribution to the momentum balance as the waves are of relatively small-amplitude in the present work, specifically A/λ ≲ 0.1....
Phase‐Integral Approximation in Momentum Space and the Bound States of an Atom The phase integral approximation of the Green's function in momentum space is investigated for an electron of negative energy (corresponding to a bound sta... MC Gutzwiller - 《Journal of Mathematical Physics》 被引...
The AO basis function |ϕiα〉 is centered at atom i. There could be multiple basis functions (labeled by n) sharing the same angular momentum quantum number l and magnetic quantum number m. The index α is an abbreviation for n, l, m. Equation (1) will be referred to as the Hk...
Their mutual interaction is blocked in the dense medium of the nucleons of the core nucleus that occupy the Fermi sphere in momentum space. This is a consequence of the antisymmetrization of the full many-fermion wave function of the entire nucleonic system. The α particle, which is ...
is a function of the electronic coordinates x and of the nuclear coordinates q. According to Born and Oppenheimer (1927), the heavier nuclei move so slowly that, in the average, electrons see only the position of nuclei and not their velocity. Therefore, Born–Oppenheimer assume that the elec...