The introduction of hyperspherical coordinates allows the separation of an $N$ -anyon Schr\"odinger equation into a hyperradial and a hyperangular part in a harmonic well. While the hyperradial part is analytically solvable, we present a systematic procedure to solve the hyperangular equation. The inclusion of a perpendicular magnetic field and inverse-square-type particle-particle interaction does not complicate the problem. The interplay of exchange statistics and conventional particle-particle interaction is emphasized.The introduction of hyperspherical coordinates allows the separation of an $N$-anyon Schr\"odinger equation into a hyperradial and a hyperangular part in a harmonic well. While the hyperradial part is analytically solvable, we present a systematic procedure to solve the hyperangular equation. The inclusion of a perpendicular magnetic field and inverse-square-type particle-particle interaction does not complicate the problem. The interplay of exchange statistics and conventional particle-particle interaction is emphasized.

Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fieldsNov 15, 19970 citations

THE SCHRÖDINGER EQUATION IN GENERALIZED COORDINATES

Elsevier eBooksJan 1, 19720 citations

The introduction of hyperspherical coordinates allows the separation of an

N

-anyon Schr\"odinger equation into a hyperradial and a hyperangular part in a harmonic well. While the hyperradial part is analytically solvable, we present a systematic procedure to solve the hyperangular equation. The inclusion of a perpendicular magnetic field and inverse-square-type particle-particle interaction does not complicate the problem. The interplay of exchange statistics and conventional particle-particle interaction is emphasized.