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IL NUOV0 CIMENTO VoL 10 A, N. 4 21 Agosto 1972 Addendum to ~ Some Remarks on the Origin of the Deviations from the Exponential Decay Law of an Unstable Particle ~. L. FONDA International Centre /or Theoretical Physics - Trieste lstituto di Fisica Teorica dell' Universit~t - Trieste G. C. GHIRARDI Istituto di Fisica Teorica dell' Universit~ - Trieste (~Vuovo Cimento, 7 A, 180 (1972)) Prof. B. SIMON has kindly pointed out to us that the proof given in our paper, according to which the equation ](t, t') ==-- Pv exp [-- iHt'] P• exp [--iHt] Pv ----0 for t, t' ~ 0 implies P• v = 0, is not correct. In fact, as we have not used the fact that the spectrum of H is bounded from below, it is possible to find a counter-example for which the proof fails. As pointed out by S~MoN, when the boundedness condition is taken into account, our claim can be rigorously proved as follows: Since H is bounded from below, exp [--iHt] is the boundary value of an oper- ator analytic function. Therefore, simply by analytic continuation from ](t, t') for t, t'> 0, there follows ](t, --t) = (1)1 exp [--iHt]PG)~(P• exp [--iHt]P~) = 0 and con- sequently P• exp [--iHt]P v = 0 for t> 0, which was our claim. Therefore all con- clusions of our paper remain valid. We thank Prof. B. SIMON for his remark. 850

Addendum to “Some remarks on the origin of the deviations from the exponential decay law of an unstable particle”

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IL NUOV0 CIMENTO VoL 10 A, N. 4 21 Agosto 1972

Addendum to ~ Some Remarks on the Origin of the Deviations from the

Exponential Decay Law of an Unstable Particle ~.

L. FONDA

International Centre /or Theoretical Physics - Trieste lsti tuto di Fisica Teorica dell' Universit~t - Trieste

G. C. GHIRARDI

Istituto di Fisica Teorica dell' Universit~ - Trieste

(~Vuovo Cimento, 7 A, 180 (1972))

Prof. B. SIMON has kindly pointed out to us that the proof given in our paper, according to which the equation ](t, t') ==-- P v exp [-- iHt'] P• exp [ - - iHt] Pv ---- 0 for t, t' ~ 0 implies P • v = 0, is not correct. In fact, as we have not used the fact that the spectrum of H is bounded from below, it is possible to find a counter-example for which the proof fails. As pointed out by S~MoN, when the boundedness condition is taken into account, our claim can be rigorously proved as follows:

Since H is bounded from below, exp [ - - iHt] is the boundary value of an oper- ator analytic function. Therefore, simply by analytic continuation from ](t, t') for t, t ' > 0, there follows ](t, - - t ) = (1)1 exp [- - iHt]PG)~(P• exp [ - - iHt]P~) = 0 and con- sequently P• exp [ - - i H t ] P v = 0 for t > 0, which was our claim. Therefore all con- clusions of our paper remain valid.

We thank Prof. B. SIMON for his remark.

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