dor_id: 41446

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100.1.#.a: Méndez Fragoso, R.; Ley Koo, Eugenio

524.#.#.a: Méndez Fragoso, R., et al. (2008). Properties of the spectra of asymmetric molecules: matrix evaluation in bases of spherical harmonics and common generating function. Revista Mexicana de Física; Vol 54, No 001. Recuperado de https://repositorio.unam.mx/contenidos/41446

245.1.0.a: Properties of the spectra of asymmetric molecules: matrix evaluation in bases of spherical harmonics and common generating function

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561.1.#.a: Facultad de Ciencias, UNAM

264.#.0.c: 2008

264.#.1.c: 2008-01-01

653.#.#.a: Asymmetric molecules; rotation spectra; matrix evaluation; spherical harmonics; Lame functions; spheroconal harmonics; generating function

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041.#.7.h: eng

520.3.#.a: The Schrodinger equation for the rotational states of asymmetric molecules is known to be separable in spheroconal coordinates and inte-̈ grable in terms of Lame functions. However, the numerical evaluation of the latter has not been developed efficiently, thereby limiting thé practical application of such solutions. In this article, the matrix evaluation of the rotational states is formulated and implemented numerically for any asymmetric molecule, using the familiar bases of spherical harmonics. The matrix of the Hamiltonian - in a frame of reference fixed in the molecule and oriented along its principal axes - is constructed in the chosen basis and shown to separate into blocks of (`+ 1)×(`+ 1) and ` × `, for each value of the angular momentum quantum number `. The diagonalization of the successive blocks leads to accurate values of eigenenergies and eigenvectors for all values of the asymmetry parameters. The connection between these rotational states and their Lame function representation is also established, identifying at the same time a common generating function for spherical harmonicś and spheroconal harmonics.

773.1.#.t: Revista Mexicana de Física; Vol 54, No 001 (2008)

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Artículo

Properties of the spectra of asymmetric molecules: matrix evaluation in bases of spherical harmonics and common generating function

Méndez Fragoso, R.; Ley Koo, Eugenio

Facultad de Ciencias, UNAM, publicado en Revista Mexicana de Física, y cosechado de Revistas UNAM

Licencia de uso

Procedencia del contenido

Entidad o dependencia
Facultad de Ciencias, UNAM
Revista
Repositorio
Contacto
Revistas UNAM. Dirección General de Publicaciones y Fomento Editorial, UNAM en revistas@unam.mx

Cita

Méndez Fragoso, R., et al. (2008). Properties of the spectra of asymmetric molecules: matrix evaluation in bases of spherical harmonics and common generating function. Revista Mexicana de Física; Vol 54, No 001. Recuperado de https://repositorio.unam.mx/contenidos/41446

Descripción del recurso

Autor(es)
Méndez Fragoso, R.; Ley Koo, Eugenio
Tipo
Artículo de Investigación
Área del conocimiento
Físico Matemáticas y Ciencias de la Tierra
Título
Properties of the spectra of asymmetric molecules: matrix evaluation in bases of spherical harmonics and common generating function
Fecha
2008-01-01
Resumen
The Schrodinger equation for the rotational states of asymmetric molecules is known to be separable in spheroconal coordinates and inte-̈ grable in terms of Lame functions. However, the numerical evaluation of the latter has not been developed efficiently, thereby limiting thé practical application of such solutions. In this article, the matrix evaluation of the rotational states is formulated and implemented numerically for any asymmetric molecule, using the familiar bases of spherical harmonics. The matrix of the Hamiltonian - in a frame of reference fixed in the molecule and oriented along its principal axes - is constructed in the chosen basis and shown to separate into blocks of (`+ 1)×(`+ 1) and ` × `, for each value of the angular momentum quantum number `. The diagonalization of the successive blocks leads to accurate values of eigenenergies and eigenvectors for all values of the asymmetry parameters. The connection between these rotational states and their Lame function representation is also established, identifying at the same time a common generating function for spherical harmonicś and spheroconal harmonics.
Tema
Asymmetric molecules; rotation spectra; matrix evaluation; spherical harmonics; Lame functions; spheroconal harmonics; generating function
Idioma
eng
ISSN
2683-2224 (digital); 0035-001X (impresa)

Enlaces