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Springer eBooks

The Eigenvalue Problem in Phase-Space

Leon W. Cohen

Published Nov 30, 2012• 0 citations
Publisher
DOI
10.1007/978-3-0348-0294-9_11

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The eigenvalue problem in phase space

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We formulate the standard quantum mechanical eigenvalue problem in quantum phase space. The equation obtained involves the c-function that corresponds to the quantum operator. We use the Wigner distribution for the phase space function. We argue that the phase space eigenvalue equation obtained has, in addition to the proper solutions, improper solutions. That is, solutions for which no wave function exists which could generate the distribution. We discuss the conditions for ascertaining whether a position momentum function is a proper phase space distribution. We call these conditions psi-representability conditions, and show that if these conditions are imposed, one extracts the correct phase space eigenfunctions. We also derive the phase space eigenvalue equation for arbitrary phase space distributions functions. © 2017 Wiley Periodicals, Inc.

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With great significance in describing the state of quantum system,the Wigner function of the spin half non-commutative Landau problem is studied in this paper.On the basis of the review of the Wigner function in the commutative space,which is subject to the *-eigenvalue equation,Hamiltonian of the spin half Landau problem in the non-commutative phase space is given.Then,energy levels and Wigner functions in the form of a matrix of the spin half Landau problem in the non-commutative phase space are obtained by means of the *-eigenvalue equation(or Moyal equation).

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自旋1/2非对易朗道问题的Wigner函数(英文)

王亚辉, 剡江峰, 袁毅

Wigner函数在对量子体系状态的描述方面具有重要的意义。 讨论了自旋1/2非对易朗道问题的Wigner函数。首先回顾了对易空间中Wigner函数所服从的星本征方程， 然后给出了非对易相空间中自旋1/2朗道问题的Hamiltonian， 最后利用星本征方程（Moyal 方程）计算了非对易相空间中自旋1/2朗道问题具有矩阵表示形式的Wigner函数及其能级。 With great significance in describing the state of quantum system, the Wigner function of the spin half noncommutative Landau problem is studied in this paper. On the basis of the review of the Wigner function in the commutative space, which is subject to the *eigenvalue equation, Hamiltonian of the spin half Landau problem in the noncommutative phase space is given. Then, energy levels and Wigner functions in the form of a matrix of the spin half Landau problem in the noncommutative phase space are obtained by means of the *-eigenvalue equation (or Moyal equation).

原子核物理评论•Dec 20, 2011•0 citations
We formulate the standard quantum mechanical eigenvalue problem in quantum phase space. The equation obtained involves the c-function that corresponds to the quantum operator. We use the Wigner distribution for the phase space function. We argue that the phase space eigenvalue equation obtained has, in addition to the proper solutions, improper solutions. That is, solutions for which no wave function exists which could generate the distribution. We discuss the conditions for ascertaining whether a position momentum function is a proper phase space distribution. We call these conditions psi-representability conditions, and show that if these conditions are imposed, one extracts the correct phase space eigenfunctions. We also derive the phase space eigenvalue equation for arbitrary phase space distributions functions. © 2017 Wiley Periodicals, Inc.
With great significance in describing the state of quantum system,the Wigner function of the spin half non-commutative Landau problem is studied in this paper.On the basis of the review of the Wigner function in the commutative space,which is subject to the *-eigenvalue equation,Hamiltonian of the spin half Landau problem in the non-commutative phase space is given.Then,energy levels and Wigner functions in the form of a matrix of the spin half Landau problem in the non-commutative phase space are obtained by means of the *-eigenvalue equation(or Moyal equation).
Wigner函数在对量子体系状态的描述方面具有重要的意义。 讨论了自旋1/2非对易朗道问题的Wigner函数。首先回顾了对易空间中Wigner函数所服从的星本征方程， 然后给出了非对易相空间中自旋1/2朗道问题的Hamiltonian， 最后利用星本征方程（Moyal 方程）计算了非对易相空间中自旋1/2朗道问题具有矩阵表示形式的Wigner函数及其能级。 With great significance in describing the state of quantum system, the Wigner function of the spin half noncommutative Landau problem is studied in this paper. On the basis of the review of the Wigner function in the commutative space, which is subject to the *eigenvalue equation, Hamiltonian of the spin half Landau problem in the noncommutative phase space is given. Then, energy levels and Wigner functions in the form of a matrix of the spin half Landau problem in the noncommutative phase space are obtained by means of the *-eigenvalue equation (or Moyal equation).