Landscape of uncertainty in Hilbert space for one-particle states

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Weigert, S.;
(1996)

The functional of uncertainty J[¿] assigns to each state ¿¿> the product of the variances of the momentum and position operators. Its first and second variations are investigated. Each stationary point is located on one of a countable set of three-dimensional manifolds ... View more
  • References (13)
    13 references, page 1 of 2

    @1# M. M. Nieto and D. R. Truax, Phys. Rev. Lett. 71, 2843 ~1993!.

    @2# R. Jackiw, J. Math. Phys. 9, 339 ~1968!.

    @3# From now on the product of the variances of position and momentum operator will be referred to as ''uncertainty.''

    @4# C. Aragone, E. Chalbaud, and S. Salamo, J. Math. Phys. 17, 1963 ~1976!.

    @5# T. Opatrny´, J. Phys. A ~to be published!.

    @6# Ph. M. Morse and H. Feshbach, Methods of Theoretical Physics ~McGraw Hill, New York, 1953!, Vol. I.

    @7# For vanishing Dq or Dp, Eq. ~9! is easily seen to define position and momentum eigenstates, respectively.

    @8# D. Stoler, Phys. Rev. D 1, 3217 ~1970!.

    @9# R. F. Bishop and A. Vourdas, Phys. Rev. A 50, 4488 ~1994!.

    @10# A. Perelomov, Generalized Coherent States and Their Applications ~Springer, Berlin, 1986!.

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