### Abstract

By employing the noncompact groups SO(n,1) we show how matrix valued differential operators for the realization of the so(n,1) algebra can be used to obtain multichannel scattering via the occurrence of LS-type interaction terms. These realizations are in terms of coordinates on the hyperboloids H ^{n} regarded as cosets SO(n,1)/SO(n). The matrix-valued nature of such realizations is connected with a finite dimensional unitary irreducible representation of the compact subgroup SO(n). The associated scattering problems are solvable one dimensional ones. The interaction terms are of LS-type multiplied by Pöschl-Teller potentials, with S playing the role of the SO(n) spin. We also show that scattering Hamiltonians based on such realizations can be related to some effective Hamiltonian coming from a coupled system of slow and fast degrees of freedom after decoupling adiabatically the fast variables. The SO(n) symmetry in this picture can be identified as the residual symmetry group of the fast subsystem surviving the adiabatic decoupling. The SO(n) spin, manifesting itself through the appearance of the aforementioned irreducible representation, also originates from the fast dynamics.

Original language | English |
---|---|

Pages (from-to) | 6633-6646 |

Number of pages | 14 |

Journal | Journal of Mathematical Physics |

Volume | 36 |

Issue number | 12 |

Publication status | Published - 1995 |

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### ASJC Scopus subject areas

- Organic Chemistry

### Cite this

*Journal of Mathematical Physics*,

*36*(12), 6633-6646.

**Modified symmetry generators related to solvable scattering problems.** / Lévay, P.; Apagyi, Barnabás.

Research output: Contribution to journal › Article

*Journal of Mathematical Physics*, vol. 36, no. 12, pp. 6633-6646.

}

TY - JOUR

T1 - Modified symmetry generators related to solvable scattering problems

AU - Lévay, P.

AU - Apagyi, Barnabás

PY - 1995

Y1 - 1995

N2 - By employing the noncompact groups SO(n,1) we show how matrix valued differential operators for the realization of the so(n,1) algebra can be used to obtain multichannel scattering via the occurrence of LS-type interaction terms. These realizations are in terms of coordinates on the hyperboloids H n regarded as cosets SO(n,1)/SO(n). The matrix-valued nature of such realizations is connected with a finite dimensional unitary irreducible representation of the compact subgroup SO(n). The associated scattering problems are solvable one dimensional ones. The interaction terms are of LS-type multiplied by Pöschl-Teller potentials, with S playing the role of the SO(n) spin. We also show that scattering Hamiltonians based on such realizations can be related to some effective Hamiltonian coming from a coupled system of slow and fast degrees of freedom after decoupling adiabatically the fast variables. The SO(n) symmetry in this picture can be identified as the residual symmetry group of the fast subsystem surviving the adiabatic decoupling. The SO(n) spin, manifesting itself through the appearance of the aforementioned irreducible representation, also originates from the fast dynamics.

AB - By employing the noncompact groups SO(n,1) we show how matrix valued differential operators for the realization of the so(n,1) algebra can be used to obtain multichannel scattering via the occurrence of LS-type interaction terms. These realizations are in terms of coordinates on the hyperboloids H n regarded as cosets SO(n,1)/SO(n). The matrix-valued nature of such realizations is connected with a finite dimensional unitary irreducible representation of the compact subgroup SO(n). The associated scattering problems are solvable one dimensional ones. The interaction terms are of LS-type multiplied by Pöschl-Teller potentials, with S playing the role of the SO(n) spin. We also show that scattering Hamiltonians based on such realizations can be related to some effective Hamiltonian coming from a coupled system of slow and fast degrees of freedom after decoupling adiabatically the fast variables. The SO(n) symmetry in this picture can be identified as the residual symmetry group of the fast subsystem surviving the adiabatic decoupling. The SO(n) spin, manifesting itself through the appearance of the aforementioned irreducible representation, also originates from the fast dynamics.

UR - http://www.scopus.com/inward/record.url?scp=21844522489&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21844522489&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:21844522489

VL - 36

SP - 6633

EP - 6646

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

SN - 0022-2488

IS - 12

ER -