Il Nuovo Cimento A (1965-1970)

, Volume 48, Issue 4, pp 997–1007 | Cite as

A reinterpretation of the notion of localization

  • A. J. Kálnay
  • B. P. Toledo


Several reasons suggest that the difficulties to obtain the position operator in relativistic quantum mechanics are caused by the hypothesis that the measurable values of a component of the position are real numbers instead of regions of space of the order of a Compton wave length. We show how to develop the idea by using nonnormal operators and prove that this is consistent with reasonable requirements of position. The use of non-Hermitian and nonnormal operators in quantum mechanics is discussed.


Position Operator Hermitian Operator Relativistic Quantum Mechanic Space Rotation Reasonable Requirement 
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Новая интерпретация понятия локализации


Высказываются некоторые аргументы, что трудности, связанные с получением оператора положения в релятивистской квантовой механике, обусловлены гипотезой, что измеряемые значания компоненты радиуса-вектора представляют вещественные числа, а не области пространства, порядка Комптоновскои длины волны. Мы показываем, чак развить эту идею, используя ненормальные операторы, и докаываем, что это согласуется с разумными требованиями положения. Обсуждается использование неэрмитовских и ненормальных операторов в квантовой механике.


Molti motivi suggeriscono che le difficoltà nell’ottenere gli operatori di posizione in meccanica quantistica relativistica sono causate dall’ipotesi che i valori misurabili di una componente della posizione siano numeri reali invece che regioni dello spazio dell’ordine della lunghezza d’onda Compton. Si mostra come sviluppare quest’idea usando operatori non normali e si dimostra che ciò è compatibile con ragionevoli esigenze di posizione. Si discute l’uso di operatori non hermitiani e non normali in meccanica quantistica.


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Copyright information

© Società Italiana di Fisica 1967

Authors and Affiliations

  • A. J. Kálnay
    • 1
  • B. P. Toledo
    • 1
  1. 1.IMAFUniversidad Nacional de CórdobaCórdobaArgentina

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