An approach to establish the connection between configuration and su(n + 1) algebraic spaces in molecular physics: application to ammonia
An approach aimed to connect configuration and algebraic spaces is discussed. This approach emerges as the need to translate a vibrational description in configuration space to an algebraic representation based on unitary dynamical algebras, where a straightforward connection does not exist e.g. the...
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| Autor*in: |
Santiago, R. D [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Rechteinformationen: |
Nutzungsrecht: © 2017 Informa UK Limited, trading as Taylor & Francis Group 2017 |
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| Schlagwörter: |
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| Übergeordnetes Werk: |
Enthalten in: Molecular physics - London : Taylor & Francis, 1958, 115(2017), 24, Seite 3206 |
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| Übergeordnetes Werk: |
volume:115 ; year:2017 ; number:24 ; pages:3206 |
| Links: |
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| DOI / URN: |
10.1080/00268976.2017.1358829 |
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| 520 | |a An approach aimed to connect configuration and algebraic spaces is discussed. This approach emerges as the need to translate a vibrational description in configuration space to an algebraic representation based on unitary dynamical algebras, where a straightforward connection does not exist e.g. the vibron model case. Our method is based on the mapping of the algebraic to configuration states, a premise that allows arbitrary operators in configuration to be expanded in terms of generators of the dynamical algebra. The coefficients are determined through a minimisation procedure and given in terms of matrix elements defined in configuration space. We apply the general formalism to the Morse potential, representing anharmonic vibrations in a molecule, as a benchmark case where a dynamical symmetry exits, and to the symmetric double-Morse potential, representing vibrations that can tunnel through a potential barrier, as an example in which a dynamical symmetry is not present. We discuss how the tunnelling effect in the double Morse can be described very simply in the su(2) algebraic representation, taking the ammonia inversion vibrational spectrum as an example. | ||
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| 650 | 4 | |a algebraic realisation | |
| 650 | 4 | |a Second quantisation | |
| 650 | 4 | |a morse potential | |
| 650 | 4 | |a ammonia | |
| 650 | 4 | |a double minimum potential | |
| 650 | 4 | |a configuration space | |
| 650 | 4 | |a double morse potential | |
| 650 | 4 | |a Algebra | |
| 650 | 4 | |a Configurations | |
| 650 | 4 | |a Molecular physics | |
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| 650 | 4 | |a Anharmonicity | |
| 650 | 4 | |a Ammonia | |
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| 650 | 4 | |a Morse potential | |
| 650 | 4 | |a Symmetry | |
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approach to establish the connection between configuration and su(n + 1) algebraic spaces in molecular physics: application to ammonia |
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An approach to establish the connection between configuration and su(n + 1) algebraic spaces in molecular physics: application to ammonia |
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An approach aimed to connect configuration and algebraic spaces is discussed. This approach emerges as the need to translate a vibrational description in configuration space to an algebraic representation based on unitary dynamical algebras, where a straightforward connection does not exist e.g. the vibron model case. Our method is based on the mapping of the algebraic to configuration states, a premise that allows arbitrary operators in configuration to be expanded in terms of generators of the dynamical algebra. The coefficients are determined through a minimisation procedure and given in terms of matrix elements defined in configuration space. We apply the general formalism to the Morse potential, representing anharmonic vibrations in a molecule, as a benchmark case where a dynamical symmetry exits, and to the symmetric double-Morse potential, representing vibrations that can tunnel through a potential barrier, as an example in which a dynamical symmetry is not present. We discuss how the tunnelling effect in the double Morse can be described very simply in the su(2) algebraic representation, taking the ammonia inversion vibrational spectrum as an example. |
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An approach aimed to connect configuration and algebraic spaces is discussed. This approach emerges as the need to translate a vibrational description in configuration space to an algebraic representation based on unitary dynamical algebras, where a straightforward connection does not exist e.g. the vibron model case. Our method is based on the mapping of the algebraic to configuration states, a premise that allows arbitrary operators in configuration to be expanded in terms of generators of the dynamical algebra. The coefficients are determined through a minimisation procedure and given in terms of matrix elements defined in configuration space. We apply the general formalism to the Morse potential, representing anharmonic vibrations in a molecule, as a benchmark case where a dynamical symmetry exits, and to the symmetric double-Morse potential, representing vibrations that can tunnel through a potential barrier, as an example in which a dynamical symmetry is not present. We discuss how the tunnelling effect in the double Morse can be described very simply in the su(2) algebraic representation, taking the ammonia inversion vibrational spectrum as an example. |
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An approach aimed to connect configuration and algebraic spaces is discussed. This approach emerges as the need to translate a vibrational description in configuration space to an algebraic representation based on unitary dynamical algebras, where a straightforward connection does not exist e.g. the vibron model case. Our method is based on the mapping of the algebraic to configuration states, a premise that allows arbitrary operators in configuration to be expanded in terms of generators of the dynamical algebra. The coefficients are determined through a minimisation procedure and given in terms of matrix elements defined in configuration space. We apply the general formalism to the Morse potential, representing anharmonic vibrations in a molecule, as a benchmark case where a dynamical symmetry exits, and to the symmetric double-Morse potential, representing vibrations that can tunnel through a potential barrier, as an example in which a dynamical symmetry is not present. We discuss how the tunnelling effect in the double Morse can be described very simply in the su(2) algebraic representation, taking the ammonia inversion vibrational spectrum as an example. |
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An approach to establish the connection between configuration and su(n + 1) algebraic spaces in molecular physics: application to ammonia |
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