On the 'orthogonalization' of the minimum uncertainty states between the position and the rational function of the momentum

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Other Title
  • 「位置」と「運動量の有理関数」の同時測定の作用素測度とそれに関連した2種類の相対エントロピーについて(第5回『非平衡系の統計物理』シンポジウム)
  • On the orthogonalization of the minimum uncertainty states between the position and the rational function of the momomentum

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Abstract

In this paper, a method of the extension of a Hilbert space is proposed for a formal orthogonalization of the eigenvector system of the operator Q+ig(P) where Q denotes the position-coordinate operator and the and g(P) is a kind of rational function of the momentum operator, in other words, for the orthogonalization of the minimum uncertainty states between Q and g(P). This kind of orthogonalization is based on the 'commutabilization' between Q and g(P) by the space extension by tensor product and the projection into the analogue of the vacuum vector in the additional space. Especially, the special case with g(P)=-kP^<-1>, which is corresponding to a kind of Naimark extension of the continuous wavelet transfonntion, is investiceted in detail.

Journal

  • 物性研究

    物性研究 71 (5), 903-909, 1999-02-20

    物性研究刊行会

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