Realization of dynamical group for a symmetric well potential tan 2(πrx/a) and its controllability

Shi Hai Dong; M. Lozada-Cassou; Marco A. Arjona L

doi:10.1142/s0217751x06033015

Realization of dynamical group for a symmetric well potential tan ²(πrx/a) and its controllability

Shi Hai Dong, M. Lozada-Cassou, Marco A. Arjona L

Research output: Contribution to journal › Article › peer-review

Abstract

The exact solutions of quantum system with a symmetric well potential V(x) = D tan² (πx/a) are obtained. The ladder operators are constructed directly from the normalized eigenfunctions with the factorization method. It is shown that these ladder operators satisfy the commutation relations of the generators for an su(1, 1) algebra. The infinitely deep square well and harmonic limits of this potential are briefly studied. The controllability of this system is also investigated. It is demonstrated that this system with discrete bound states can be strongly completely controlled. This may be realized theoretically by acting the creation operator K̂+ on the ground state.

Original language	English
Pages (from-to)	5833-5843
Number of pages	11
Journal	International Journal of Modern Physics A
Volume	21
Issue number	28-29
DOIs	https://doi.org/10.1142/s0217751x06033015
State	Published - 20 Nov 2006

Keywords

Controllability
Factorization method
Ladder operators, su(1, 1) algebra

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10.1142/s0217751x06033015

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abstract = "The exact solutions of quantum system with a symmetric well potential V(x) = D tan2 (πx/a) are obtained. The ladder operators are constructed directly from the normalized eigenfunctions with the factorization method. It is shown that these ladder operators satisfy the commutation relations of the generators for an su(1, 1) algebra. The infinitely deep square well and harmonic limits of this potential are briefly studied. The controllability of this system is also investigated. It is demonstrated that this system with discrete bound states can be strongly completely controlled. This may be realized theoretically by acting the creation operator {\^K}+ on the ground state.",

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AU - Dong, Shi Hai

AU - Lozada-Cassou, M.

AU - Arjona L, Marco A.

PY - 2006/11/20

Y1 - 2006/11/20

N2 - The exact solutions of quantum system with a symmetric well potential V(x) = D tan2 (πx/a) are obtained. The ladder operators are constructed directly from the normalized eigenfunctions with the factorization method. It is shown that these ladder operators satisfy the commutation relations of the generators for an su(1, 1) algebra. The infinitely deep square well and harmonic limits of this potential are briefly studied. The controllability of this system is also investigated. It is demonstrated that this system with discrete bound states can be strongly completely controlled. This may be realized theoretically by acting the creation operator K̂+ on the ground state.

AB - The exact solutions of quantum system with a symmetric well potential V(x) = D tan2 (πx/a) are obtained. The ladder operators are constructed directly from the normalized eigenfunctions with the factorization method. It is shown that these ladder operators satisfy the commutation relations of the generators for an su(1, 1) algebra. The infinitely deep square well and harmonic limits of this potential are briefly studied. The controllability of this system is also investigated. It is demonstrated that this system with discrete bound states can be strongly completely controlled. This may be realized theoretically by acting the creation operator K̂+ on the ground state.

KW - Controllability

KW - Factorization method

KW - Ladder operators, su(1, 1) algebra

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DO - 10.1142/s0217751x06033015

M3 - Artículo

SN - 0217-751X

VL - 21

SP - 5833

EP - 5843

JO - International Journal of Modern Physics A

JF - International Journal of Modern Physics A

IS - 28-29

ER -

Realization of dynamical group for a symmetric well potential tan ²(πrx/a) and its controllability

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Keywords

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