Particle in a central potential

D. Baye, M. Dufour, Benjamin Fuks E

Claude N. Cohen-Tannoudji, Bernard Diu, Franck Laloë

Alberto Galindo, P. Pascual

M. D. de Oliveira, Alexandre G. M. Schmidt

We calculate exact solutions of the Schrödinger equation for a particle constrained to move along a spherical surface and interacting with non-central potentials, namely, (i) Makarov, (ii) ring-shaped pseudo-harmonic oscillatory, and (iii) Kratzer potentials. We also study exact solutions of the Pauli equation in the same geometrical setting for a charged particle in the presence of a uniform magnetic field. In this case, the two-component spinor can adhere to the surface only if the magnetic field intensity has certain special values. The solutions of Schrödinger equations allow us to obtain exact Pauli spinors and their corresponding energy eigenvalues for the same non-central potentials.

Rocco Schiavilla

Exchange and permutation operators; symmetrizer and antisymmetrizer; two bosons or two fermions in a central potential; scattering amplitudes of two identical particles in a central potential; the Fermi gas; theory of white dwarf stars; the Thomas-Fermi approximation for many-electron atoms.

Vasily Veniaminovitch Pupyshev

We study the two-dimensional motion of a slow quantum particle in the field of a central long-range potential decaying in the limit of long distances r as the power r −β with the exponent β ∈ (1, 2). We find the low-temperature asymptotic behavior for all partial phases and the differential cross section of the particle scattering and derive a rather simple approximation for the weakly bound state energy.