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.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.

Journal of Mathematical PhysicsMar 1, 20198 citations

Two-particle states and interactions

WORLD SCIENTIFIC eBooksApr 1, 20050 citations

Two-particle states and interactions

WORLD SCIENTIFIC eBooksMay 1, 20080 citations

Pomeranchuk and topological Fermi surface instabilities from central interactions

Jorge Quintanilla, A. J. Schofield

We address at the mean field level the emergence of a Pomeranchuk instability in a uniform Fermi liquid with central particle-particle interactions. We find that Pomeranchuk instabilities with all symmetries except $l=1$ can take place if the interaction is repulsive and has a finite range ${r}_{0}$ of the order of the interparticle distance. We demonstrate this by solving the mean field equations analytically for an explicit model interaction, as well as numerical results for more realistic potentials. We find in addition to the Pomeranchuk instability other, subtler phase transitions in which the Fermi surface changes topology without rotational symmetry breaking. We argue that such interaction-driven topological transitions may be as generic to such systems as the Pomeranchuk instability.We address at the mean field level the emergence of a Pomeranchuk instability in a uniform Fermi liquid with central particle-particle interactions. We find that Pomeranchuk instabilities with all symmetries except $l=1$ can take place if the interaction is repulsive and has a finite range ${r}_{0}$ of the order of the interparticle distance. We demonstrate this by solving the mean field equations analytically for an explicit model interaction, as well as numerical results for more realistic potentials. We find in addition to the Pomeranchuk instability other, subtler phase transitions in which the Fermi surface changes topology without rotational symmetry breaking. We argue that such interaction-driven topological transitions may be as generic to such systems as the Pomeranchuk instability.

arXiv:cond-mat/0601103Physical Review BSep 28, 200689 citations

Two-particle interaction

Springer eBooksApr 6, 20081 citation

Integrability and the Conformal Bootstrap

Volker Schomerus

Conformal blocks are the central ingredient of bootstrap programme to constructing d-dimensional conformal field theories. I will show that such blocks can be mapped to eigenfunctions of a 2-particle hyperbolic Calogero-Sutherland Hamiltonian. The latter describes two coupled P\”oschl-Teller particles. Their interaction, whose strength depends smoothly on the dimension $d$ , is known to be integrable. Several consequences of this observation will be sketched before I conclude with an outlook on new perspectives for the bootstrap programme.Conformal blocks are the central ingredient of bootstrap programme to constructing d-dimensional conformal field theories. I will show that such blocks can be mapped to eigenfunctions of a 2-particle hyperbolic Calogero-Sutherland Hamiltonian. The latter describes two coupled P\”oschl-Teller particles. Their interaction, whose strength depends smoothly on the dimension $d$, is known to be integrable. Several consequences of this observation will be sketched before I conclude with an outlook on new perspectives for the bootstrap programme.

Jan 1, 20160 citations

l=1

can take place if the interaction is repulsive and has a finite range

{r}_{0}

of the order of the interparticle distance. We demonstrate this by solving the mean field equations analytically for an explicit model interaction, as well as numerical results for more realistic potentials. We find in addition to the Pomeranchuk instability other, subtler phase transitions in which the Fermi surface changes topology without rotational symmetry breaking. We argue that such interaction-driven topological transitions may be as generic to such systems as the Pomeranchuk instability.

d

, is known to be integrable. Several consequences of this observation will be sketched before I conclude with an outlook on new perspectives for the bootstrap programme.