Exact Solutions of Non-autonomous Quantum Systems With Semisimple Lie Algebraic Structure

Jie Quanlin; Wang Shunjin; Wei Lianfu

Chinese Physics C> 1998, Vol. 22> Issue(2) : 111-116

Exact Solutions of Non-autonomous Quantum Systems With Semisimple Lie Algebraic Structure

Institute of Modern Physics Southwest Jiaotong University,Chengdu 610031

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Abstract：
For quantum systems with semi-simple Lie algebraic structures,the exact solutions of the equations of motion are obtained by means of algebraic dynamics.The Hamiltonian is transformed into a linear function of Cartan operators by a set of gauge transformations. The coefficients of the gauge transformations are determined by a set of ordinary differential equations.From the inverses of these gauge transformations,the solutions of the Schrodinger equation,as well as a set of dynamic constants of motion (dynamic invariant operators) are obtained. An SU(3) model serves as an example.

References

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Jie Quanlin, Wang Shunjin and Wei Lianfu. Exact Solutions of Non-autonomous Quantum Systems With Semisimple Lie Algebraic Structure[J]. Chinese Physics C, 1998, 22(2): 111-116.

Jie Quanlin, Wang Shunjin and Wei Lianfu. Exact Solutions of Non-autonomous Quantum Systems With Semisimple Lie Algebraic Structure[J]. Chinese Physics C, 1998, 22(2): 111-116. shu

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Received: 1900-01-01
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通讯作者: 陈斌, [email protected]

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沈阳化工大学材料科学与工程学院沈阳 110142

Exact Solutions of Non-autonomous Quantum Systems With Semisimple Lie Algebraic Structure

Corresponding author: Jie Quanlin,

Institute of Modern Physics Southwest Jiaotong University,Chengdu 610031

Received Date: 1900-01-01

Accepted Date: 1900-01-01

Available Online: 1998-02-05

Abstract: For quantum systems with semi-simple Lie algebraic structures,the exact solutions of the equations of motion are obtained by means of algebraic dynamics.The Hamiltonian is transformed into a linear function of Cartan operators by a set of gauge transformations. The coefficients of the gauge transformations are determined by a set of ordinary differential equations.From the inverses of these gauge transformations,the solutions of the Schrodinger equation,as well as a set of dynamic constants of motion (dynamic invariant operators) are obtained. An SU(3) model serves as an example.

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Exact Solutions of Non-autonomous Quantum Systems With Semisimple Lie Algebraic Structure

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