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Volumn 58, Issue 6, 1998, Pages 4336-4344

Space-time properties of free-motion time-of-arrival eigenfunctions

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; INTEGRAL EQUATIONS; PHASE SPACE METHODS; PROBABILITY DENSITY FUNCTION; SET THEORY; VECTORS;

EID: 0032384931     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.58.4336     Document Type: Article
Times cited : (82)

References (35)
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    • W. Pauli, in Encyclopedia of Physics, edited by S. Flugge (Springer, Berlin, 1958), Vol. 5/1, p. 60.
    • (1958) Encyclopedia of Physics , vol.5 , pp. 60
    • Pauli, W.1
  • 4
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    • Ann. Phys. (N.Y.)G. R. Allcock53, 286 (1969);
    • (1969) , vol.53 , pp. 286
    • Allcock, G.R.1
  • 5
    • 0347355107 scopus 로고
    • Ann. Phys. (N.Y.)G. R. Allcock53, 311 (1969).
    • (1969) , vol.53 , pp. 311
    • Allcock, G.R.1
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    • 85037179572 scopus 로고    scopus 로고
    • M. Toller, e-print quant-ph/9805030.
    • Toller, M.1
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    • JPHAC5
    • J. León, J. Phys. A 40, 4791 (1997).JPHAC5
    • (1997) J. Phys. A , vol.40 , pp. 4791
    • León, J.1
  • 22
  • 24
    • 85037253995 scopus 로고    scopus 로고
    • The “flux” is evaluated with the standard expression, (Formula presented) Neither this “flux” nor the “probability density” (Formula presented) obtained from Eq. (32) have the proper dimensions. This is due to the “continuum” normalization used for the eigenstates of (Formula presented) which are not square integrable. The appropriate dimensions are of course obtained by integrating these objects over time to form wave packets
    • The “flux” is evaluated with the standard expression, (Formula presented) Neither this “flux” nor the “probability density” (Formula presented) obtained from Eq. (32) have the proper dimensions. This is due to the “continuum” normalization used for the eigenstates of (Formula presented) which are not square integrable. The appropriate dimensions are of course obtained by integrating these objects over time to form wave packets.
  • 25
    • 85037185492 scopus 로고    scopus 로고
    • According to the terminology of Ref
    • According to the terminology of Ref. 11, any self-adjoint operator is “sharp.” However, referring to the eigenstates of the self-adjoint time operators, we use the sharp/unsharp concept in a way closer to the conventional usage of the words. Being sharp is “having an edge or point” or “being abrupt.”
  • 26
    • 85037239751 scopus 로고    scopus 로고
    • A similar construction was carried out by Paul with a flat weighting function instead of a Gaussian. However, while he dismissed these states because they do not belong to (Formula presented) this is not essential to construct a POVM
    • A similar construction was carried out by Paul with a flat weighting function instead of a Gaussian. However, while he dismissed these states because they do not belong to (Formula presented) this is not essential to construct a POVM.


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