By Max Jammer

Jammer, Max The philosophy of quantum mechanics (New York, Wiley [1974)(ISBN 0471439584)

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Extra resources for The philosophy of quantum mechanics; the interpretations of quantum mechanics in historical perspective.

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Heisenberg now felt that the solution of the problem lay in this statement. For if it can be shown that the theory denies the strict observability of the trajectory of the particle (position and momentum) and instead regards the "observed" phenomenon in the Wilson chamber as only a discrete sequence of imprecisely defined positions, as indicated by the condensed water droplets, a consistent connection between the mathematical formalism and observational experience may be established. & Witsch, Cologne, Berlm, 1970), pp.

Bodiou, "Renforcement des relations d'incertitude en statistique quantique par I'introduction d'un coefficient complexe de corrtlation," Comptes Rendus 228, 54C542 (1949); A. Gamba, "Sulla relazione di indeterminazione," Nuow Cimento 7, 378-379 (1950); "The uncertainty relation," Nature 166, 653-654 (1950); L. Castoldi, "Sulla relazione di indeterminazione," Numo Cimento 7, 961-962 (1950); R. L. Reed and M. Dresden, "Thee uncertainty principle for an arbitrary number of variables," Physical Reuiew 79, 2 W 2 0 1 (1950); Bulletin of the American Physical Society 25, 3 (1950); G.

Robertson, "The uncertainty principle," Physical Rmiew 34, 163-164 (1929). While an assistant at that time to Hermann Weyl (who spent the academic year 1928-1929 at Princeton) Robertson translated into English Weyl's treatise mentioned in Ref. 14. 72 Subsequent Derivations of the Indeterminacy Relations The Indeterminacy Relations strengthened, since for any two self-adjoint operators A and B and for any state rC, by A , = A - ( A ) so that the standard deviation AA is (A,')"' (and similarly for B,) and D defined by D = A , + ihB,, where h is a real number, it easily follows that Even though the last squared term in Schrodinger's formula often vanishes, as it does in the case of all optimal simultaneous measurements of canonically conjugate variables, Schrodinger's formula constitutes an important refinement of Robertson's result.

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