INVESTIGADORES
LAMBERTI Pedro Walter
artículos
Título:
A study of the orthogonal polynomials associated with the quantum harmonic oscillator on constant curvature spaces
Autor/es:
CHRISTOPHE VIGNAT; PEDRO W. LAMBERTI
Revista:
JOURNAL OF MATHEMATICAL PHYSICS
Editorial:
AMER INST PHYSICS
Referencias:
Año: 2009 vol. 50 p. 1035141 - 10351410
ISSN:
0022-2488
Resumen:
Recently, Cariñena, et al. [Ann. Phys. 322, 434, (2007)] introduced a new family of
orthogonal polynomials that appear in the wave functions of the quantum harmonic
oscillator in two-dimensional constant curvature spaces. They are a generalization
of the Hermite polynomials and will be called curved Hermite polynomials in the
following. We show that these polynomials are naturally related to the relativistic
Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)],
and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between
the solutions of the quantum harmonic oscillator on negative curvature spaces and
on positive curvature spaces. At last, we show a maximum entropy property for the
ground states of these oscillators and thus are Jacobi polynomials.
and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between
the solutions of the quantum harmonic oscillator on negative curvature spaces and
on positive curvature spaces. At last, we show a maximum entropy property for the
ground states of these oscillators and thus are Jacobi polynomials.
following. We show that these polynomials are naturally related to the relativistic
Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)],
and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between
the solutions of the quantum harmonic oscillator on negative curvature spaces and
on positive curvature spaces. At last, we show a maximum entropy property for the
ground states of these oscillators and thus are Jacobi polynomials.
and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between
the solutions of the quantum harmonic oscillator on negative curvature spaces and
on positive curvature spaces. At last, we show a maximum entropy property for the
ground states of these oscillators and thus are Jacobi polynomials.
orthogonal polynomials that appear in the wave functions of the quantum harmonic
oscillator in two-dimensional constant curvature spaces. They are a generalization
of the Hermite polynomials and will be called curved Hermite polynomials in the
following. We show that these polynomials are naturally related to the relativistic
Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)],
and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between
the solutions of the quantum harmonic oscillator on negative curvature spaces and
on positive curvature spaces. At last, we show a maximum entropy property for the
ground states of these oscillators and thus are Jacobi polynomials.
and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between
the solutions of the quantum harmonic oscillator on negative curvature spaces and
on positive curvature spaces. At last, we show a maximum entropy property for the
ground states of these oscillators and thus are Jacobi polynomials.
following. We show that these polynomials are naturally related to the relativistic
Hermite polynomials introduced by Aldaya et al. [Phys. Lett. A 156, 381 (1991)],
and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between
the solutions of the quantum harmonic oscillator on negative curvature spaces and
on positive curvature spaces. At last, we show a maximum entropy property for the
ground states of these oscillators and thus are Jacobi polynomials.
and thus are Jacobi polynomials. Moreover, we exhibit a natural bijection between
the solutions of the quantum harmonic oscillator on negative curvature spaces and
on positive curvature spaces. At last, we show a maximum entropy property for the
ground states of these oscillators and thus are Jacobi polynomials.