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Erratum to: “Protective measurements and Bohm trajectories” [Phys. Lett. A 263 (1999) 137–146]
21 February 2000
Physics Letters A 266 Ž2000. 216–217 www.elsevier.nlrlocaterphysleta
Erratum
Erratum to: ‘‘Protective measurements and Bohm trajectories’’ wPhys. Lett. A 263 ž1999/ 137–146x q Yakir Aharonov a
a,b,c
, Berthold-Georg Englert
C ini Ž t , x , X . s l
y1 r2
1 2
cos Ž p xrl
= Ž 2rp .
1r4
Žb.
.
a Ž t . d Pr"
1r2
Žc.
2
=eya Ž t .Ž X d P r " . . Ž 5. Subsequent references to the first line and second line in Ž5. are then consistent. 2. On p. 141, left column, equation Ž23., the factor Ž2rp .1r4 at the end of the first line should be moved to the second line, immediately after the multiplication sign. 3.
Ža.
On p. 142, left column, replace equation Ž30. by m l X E f Ž trT . ÕŽ t, x, X . se l "T Et 8 tan Ž 12 p xrl . = p3
=tan Ž p < x
.
5
PII of original article S0375-9601Ž99.00628-3 Corresponding author. E-mail address: [email protected] ŽB.-G. Englert..
On p. 142, right column, replace equation Ž32. by d X BM Ž t . y D X Ž t .
d XŽ t. ml Ed X Ž t . se f Ž trT . "T Et 4 w p Ž 1 y < x BM Ž t .
½
.
5
=tan Ž 12 p < x BM
= 1 y p Ž 1 y < x
On page 143, left column, second line before equation Ž34., replace ‘‘factor in the second line of Ž30.’’ by ‘‘curlybracket factor of Ž30.’’. On page 143, right column, caption to Fig. 4, replace ‘‘factor in the second line of Eq. Ž30.’’ by ‘‘curly-bracket factor of Eq. Ž30.’’.
dt
1 2
)
a,d
4.
½
q
, Marlan O. Scully
Institute for Quantum Studies and Department of Physics, Texas A & M UniÕersity, College Station, TX 77843-4242, USA b Physics Department, UniÕersity of South Carolina, Columbia, SC 29208, USA c School of Physics and Astronomy, Tel-AÕiÕ UniÕersity, Tel-AÕiÕ 69978, Israel d Max-Planck-Institut fur ¨ Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
1. On p. 139, left column, equation Ž5. should read
Ža.
a,d,)
Žb.
Ž 30 .
5.
On p. 142, right column, in the sentence right after equation Ž32. replace ‘‘the x BM dependent factor in the second line’’ by ‘‘the x BM dependent curlybracket factor’’.
On p. 142, right column, the sentence right after equation Ž32. should end with ‘‘the right-
0375-9601r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 6 0 1 Ž 0 0 . 0 0 0 2 4 - 4
Y. AharonoÕ et al.r Physics Letters A 266 (2000) 216–217
6.
7.
hand side cannot exceed Ž8rp 2 . e Ž mrM . =Ž l d Pr" ..’’, rather than ‘‘the right-hand side cannot exceed Ž8rp 2 . e Ž mrM .- Ž l d Pr" ..’’. On p. 143, right column, top line Žjust below Fig. 4., replace ‘‘end Section 2’’ by ‘‘end of Section 2’’. On p. 143, right column, replace equation Ž37. by x BM Ž T . y x BM Ž yT . s
T
HyTd t Õ Ž t , x
F 0.06 f Ž 0 . e
BM
Ž t . , X BM Ž t . .
m l X BM "T
=2 l max
Ž 37 .
8.
217
On p. 145, right column, the line before equation ŽA.7., replace ‘‘Ž43a. and Ž43b.’’ by ‘‘ŽA.6a. and ŽA.6b.’’. 9. On p. 146, left column, second line from the top, replace ‘‘It gives the second line of Ž31.’’ by ‘‘It gives the term in the second and third line of Ž31.’’. 10. On p. 146, in reference w1x Ža. delete ‘‘Part I,’’; Žb. replace ‘‘Part II,’’ by ‘‘ibid.’’.
Physics Letters A 266 Ž2000. 216–217 www.elsevier.nlrlocaterphysleta
Erratum
Erratum to: ‘‘Protective measurements and Bohm trajectories’’ wPhys. Lett. A 263 ž1999/ 137–146x q Yakir Aharonov a
a,b,c
, Berthold-Georg Englert
C ini Ž t , x , X . s l
y1 r2
1 2
cos Ž p xrl
= Ž 2rp .
1r4
Žb.
.
a Ž t . d Pr"
1r2
Žc.
2
=eya Ž t .Ž X d P r " . . Ž 5. Subsequent references to the first line and second line in Ž5. are then consistent. 2. On p. 141, left column, equation Ž23., the factor Ž2rp .1r4 at the end of the first line should be moved to the second line, immediately after the multiplication sign. 3.
Ža.
On p. 142, left column, replace equation Ž30. by m l X E f Ž trT . ÕŽ t, x, X . se l "T Et 8 tan Ž 12 p xrl . = p3
=tan Ž p < x
.
5
PII of original article S0375-9601Ž99.00628-3 Corresponding author. E-mail address: [email protected] ŽB.-G. Englert..
On p. 142, right column, replace equation Ž32. by d X BM Ž t . y D X Ž t .
d XŽ t. ml Ed X Ž t . se f Ž trT . "T Et 4 w p Ž 1 y < x BM Ž t .
½
.
5
=tan Ž 12 p < x BM
= 1 y p Ž 1 y < x
On page 143, left column, second line before equation Ž34., replace ‘‘factor in the second line of Ž30.’’ by ‘‘curlybracket factor of Ž30.’’. On page 143, right column, caption to Fig. 4, replace ‘‘factor in the second line of Eq. Ž30.’’ by ‘‘curly-bracket factor of Eq. Ž30.’’.
dt
1 2
)
a,d
4.
½
q
, Marlan O. Scully
Institute for Quantum Studies and Department of Physics, Texas A & M UniÕersity, College Station, TX 77843-4242, USA b Physics Department, UniÕersity of South Carolina, Columbia, SC 29208, USA c School of Physics and Astronomy, Tel-AÕiÕ UniÕersity, Tel-AÕiÕ 69978, Israel d Max-Planck-Institut fur ¨ Quantenoptik, Hans-Kopfermann-Strasse 1, 85748 Garching, Germany
1. On p. 139, left column, equation Ž5. should read
Ža.
a,d,)
Žb.
Ž 30 .
5.
On p. 142, right column, in the sentence right after equation Ž32. replace ‘‘the x BM dependent factor in the second line’’ by ‘‘the x BM dependent curlybracket factor’’.
On p. 142, right column, the sentence right after equation Ž32. should end with ‘‘the right-
0375-9601r00r$ - see front matter q 2000 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 5 - 9 6 0 1 Ž 0 0 . 0 0 0 2 4 - 4
Y. AharonoÕ et al.r Physics Letters A 266 (2000) 216–217
6.
7.
hand side cannot exceed Ž8rp 2 . e Ž mrM . =Ž l d Pr" ..’’, rather than ‘‘the right-hand side cannot exceed Ž8rp 2 . e Ž mrM .- Ž l d Pr" ..’’. On p. 143, right column, top line Žjust below Fig. 4., replace ‘‘end Section 2’’ by ‘‘end of Section 2’’. On p. 143, right column, replace equation Ž37. by x BM Ž T . y x BM Ž yT . s
T
HyTd t Õ Ž t , x
F 0.06 f Ž 0 . e
BM
Ž t . , X BM Ž t . .
m l X BM "T
=2 l max
Ž 37 .
8.
217
On p. 145, right column, the line before equation ŽA.7., replace ‘‘Ž43a. and Ž43b.’’ by ‘‘ŽA.6a. and ŽA.6b.’’. 9. On p. 146, left column, second line from the top, replace ‘‘It gives the second line of Ž31.’’ by ‘‘It gives the term in the second and third line of Ž31.’’. 10. On p. 146, in reference w1x Ža. delete ‘‘Part I,’’; Žb. replace ‘‘Part II,’’ by ‘‘ibid.’’.