Phase-space representation of quantum state vectors: The relative-state approach and the displacement-operator approach

Journal of Mathematical Physics

Volumn 40, Issue 8, 1999, Pages 3718-3722

  Masashi, Ban ^a  

^a HITACHI LTD   (Japan)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0033177059     PISSN: 00222488     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.532956     Document Type: Article

References (22)

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6. Any eiganstate of an unbounded operator with continuous spectrum, such as position and momentum operators, cannot be an element of a Hubert space. Such a state vector is rigorously treated by introducing a rigged Hilbert space (or Gel'fand triplets) [see A. Böhm, The Rigged Hilben Space and Quantum Mechanics (Springer-Verlag, Berlin, 1978); A. Böhm and M. Gadella, Dirac Kets, Gamov Vectors, and Gel'fand Triplets (Springer-Verlag, Berlin, 1989)].
7. Any eiganstate of an unbounded operator with continuous spectrum, such as position and momentum operators, cannot be an element of a Hubert space. Such a state vector is rigorously treated by introducing a rigged Hilbert space (or Gel'fand triplets) [see A. Böhm, The Rigged Hilben Space and Quantum Mechanics (Springer-Verlag, Berlin, 1978); A. Böhm and M. Gadella, Dirac Kets, Gamov Vectors, and Gel'fand Triplets (Springer-Verlag, Berlin, 1989)].
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