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  1. W. E. Lamb, Phys. Rev. 85, 259 (1952), Secs. 51 and 54(d). See also S. J. Brodsky and R. G. Parsons, ibid. 163, 134 (1967).
    [Crossref]
  2. A lucid plausibility argument is given by H. A. Bethe and E. E. Salpeter, in Encyclopedia of Physics Vol. 35, S. Flügge, Ed., (Springer-Verlag, Berlin, 1957), Sec. 47β.
  3. This simple conservation law must have been noticed by many; I first heard it from E. C. Lerner. An obvious analog holds when the two charges are not equal and opposite.
  4. For a situation with some parallels, see E. Breitenberger, Am. J. Phys. 36, 504 (1968).
    [Crossref]
  5. Recent references: H. H. Denman, J. Math. Phys. 6, 1611 (1965) and J. Math. Phys. 7, 1910 (1966); C. A. López, Nuovo Cimento 40, 19 (1965); B. Podolsky, Am. J. Phys. 34, 42 (1966).
    [Crossref]
  6. Physically, this term corresponds to an electrodynamic Stark effect [W. Wien, Ann. Physik 49, 842 (1916)] caused by the joint motion of the two charges across the magnetic-field lines (cf. also Lamb, Ref. 1); it has the requisite form −e(−E·r) for a constant, homogeneous electric field E = (P/M) ×B.
    [Crossref]
  7. V. Berestetsky, Zh. Eksperim. i Teor. Fiz. 19, 1130 (1949) (in Russian). Also Bethe and Salpeter, Ref. 2, Sec. 23.
  8. L. I. Schiff and H. Snyder, Phys. Rev. 55, 59 (1939); D. Harting and P. F. A. Klinkenberg, Physica 14, 669 (1949); and further references given therein.
    [Crossref]

1968 (1)

For a situation with some parallels, see E. Breitenberger, Am. J. Phys. 36, 504 (1968).
[Crossref]

1965 (1)

Recent references: H. H. Denman, J. Math. Phys. 6, 1611 (1965) and J. Math. Phys. 7, 1910 (1966); C. A. López, Nuovo Cimento 40, 19 (1965); B. Podolsky, Am. J. Phys. 34, 42 (1966).
[Crossref]

1952 (1)

W. E. Lamb, Phys. Rev. 85, 259 (1952), Secs. 51 and 54(d). See also S. J. Brodsky and R. G. Parsons, ibid. 163, 134 (1967).
[Crossref]

1949 (1)

V. Berestetsky, Zh. Eksperim. i Teor. Fiz. 19, 1130 (1949) (in Russian). Also Bethe and Salpeter, Ref. 2, Sec. 23.

1939 (1)

L. I. Schiff and H. Snyder, Phys. Rev. 55, 59 (1939); D. Harting and P. F. A. Klinkenberg, Physica 14, 669 (1949); and further references given therein.
[Crossref]

1916 (1)

Physically, this term corresponds to an electrodynamic Stark effect [W. Wien, Ann. Physik 49, 842 (1916)] caused by the joint motion of the two charges across the magnetic-field lines (cf. also Lamb, Ref. 1); it has the requisite form −e(−E·r) for a constant, homogeneous electric field E = (P/M) ×B.
[Crossref]

Berestetsky, V.

V. Berestetsky, Zh. Eksperim. i Teor. Fiz. 19, 1130 (1949) (in Russian). Also Bethe and Salpeter, Ref. 2, Sec. 23.

Bethe, H. A.

A lucid plausibility argument is given by H. A. Bethe and E. E. Salpeter, in Encyclopedia of Physics Vol. 35, S. Flügge, Ed., (Springer-Verlag, Berlin, 1957), Sec. 47β.

Breitenberger, E.

For a situation with some parallels, see E. Breitenberger, Am. J. Phys. 36, 504 (1968).
[Crossref]

Denman, H. H.

Recent references: H. H. Denman, J. Math. Phys. 6, 1611 (1965) and J. Math. Phys. 7, 1910 (1966); C. A. López, Nuovo Cimento 40, 19 (1965); B. Podolsky, Am. J. Phys. 34, 42 (1966).
[Crossref]

Lamb, W. E.

W. E. Lamb, Phys. Rev. 85, 259 (1952), Secs. 51 and 54(d). See also S. J. Brodsky and R. G. Parsons, ibid. 163, 134 (1967).
[Crossref]

Salpeter, E. E.

A lucid plausibility argument is given by H. A. Bethe and E. E. Salpeter, in Encyclopedia of Physics Vol. 35, S. Flügge, Ed., (Springer-Verlag, Berlin, 1957), Sec. 47β.

Schiff, L. I.

L. I. Schiff and H. Snyder, Phys. Rev. 55, 59 (1939); D. Harting and P. F. A. Klinkenberg, Physica 14, 669 (1949); and further references given therein.
[Crossref]

Snyder, H.

L. I. Schiff and H. Snyder, Phys. Rev. 55, 59 (1939); D. Harting and P. F. A. Klinkenberg, Physica 14, 669 (1949); and further references given therein.
[Crossref]

Wien, W.

Physically, this term corresponds to an electrodynamic Stark effect [W. Wien, Ann. Physik 49, 842 (1916)] caused by the joint motion of the two charges across the magnetic-field lines (cf. also Lamb, Ref. 1); it has the requisite form −e(−E·r) for a constant, homogeneous electric field E = (P/M) ×B.
[Crossref]

Am. J. Phys. (1)

For a situation with some parallels, see E. Breitenberger, Am. J. Phys. 36, 504 (1968).
[Crossref]

Ann. Physik (1)

Physically, this term corresponds to an electrodynamic Stark effect [W. Wien, Ann. Physik 49, 842 (1916)] caused by the joint motion of the two charges across the magnetic-field lines (cf. also Lamb, Ref. 1); it has the requisite form −e(−E·r) for a constant, homogeneous electric field E = (P/M) ×B.
[Crossref]

J. Math. Phys. (1)

Recent references: H. H. Denman, J. Math. Phys. 6, 1611 (1965) and J. Math. Phys. 7, 1910 (1966); C. A. López, Nuovo Cimento 40, 19 (1965); B. Podolsky, Am. J. Phys. 34, 42 (1966).
[Crossref]

Phys. Rev. (2)

W. E. Lamb, Phys. Rev. 85, 259 (1952), Secs. 51 and 54(d). See also S. J. Brodsky and R. G. Parsons, ibid. 163, 134 (1967).
[Crossref]

L. I. Schiff and H. Snyder, Phys. Rev. 55, 59 (1939); D. Harting and P. F. A. Klinkenberg, Physica 14, 669 (1949); and further references given therein.
[Crossref]

Zh. Eksperim. i Teor. Fiz. (1)

V. Berestetsky, Zh. Eksperim. i Teor. Fiz. 19, 1130 (1949) (in Russian). Also Bethe and Salpeter, Ref. 2, Sec. 23.

Other (2)

A lucid plausibility argument is given by H. A. Bethe and E. E. Salpeter, in Encyclopedia of Physics Vol. 35, S. Flügge, Ed., (Springer-Verlag, Berlin, 1957), Sec. 47β.

This simple conservation law must have been noticed by many; I first heard it from E. C. Lerner. An obvious analog holds when the two charges are not equal and opposite.

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Equations (16)

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m 1 r ¨ 1 = - 1 V + e r ˙ 1 × B , m 2 r ¨ 2 = - 2 V - e r ˙ 2 × B .
M R ˙ - e B × r = const ,
L = 1 2 m 1 v 1 2 + 1 2 m 2 v 2 2 + 1 2 e [ v 1 · ( B × r 1 ) - v 2 · ( B × r 2 ) ] - V ( r ) ,
p 1 = m 1 v 1 + 1 2 e B × r 1 , p 2 = m 2 v 2 - 1 2 e B × r 2 ,
1 2 e ( d / d t ) [ ( B × r 1 ) · r 2 ] = 1 2 e [ - v 1 · ( B × r 2 ) + v 2 · ( B × r 1 ) ]
L = 1 2 m 1 v 1 2 + 1 2 m 2 v 2 2 - 1 2 e ( v 1 + v 2 ) · ( B × r ) - V ( r ) ,
p 1 = m 1 v 1 - 1 2 e B × r , p 2 = m 2 v 2 - 1 2 e B × r .
p 1 + p 2 = P = const .
L = 1 2 R ˙ 2 + 1 2 μ r ˙ 2 - 1 2 e [ 2 R ˙ + r ˙ ( m 1 - m 2 ) / M ] · ( B × r ) - V ( r ) ,
P = M R ˙ - e B × r , p = μ r ˙ - 1 2 e [ ( m 1 - m 2 ) / M ] B × r .
L = P · R ˆ + p · r ˙ - 1 2 M R ˙ 2 - 1 2 μ r 2 - V ( r ) .
H = 1 2 M R ˙ 2 + 1 2 μ r ˙ 2 + V ( r ) ,
H int = e 2 2 M ( B × r ) 2 + 1 2 μ [ p + 1 2 e ( m 1 - m 2 M B ) × r ] 2 + V ( r ) ,
H 2 = ( 1 / 2 m 2 ) [ p + 1 2 e B × r ] 2 + V ( r ) ,
ω L = e B 2 μ m 1 - m 2 M = e B 2 m 2 ( 1 - m 2 m 1 )
B 2 2 M + B 2 8 μ ( m 1 - m 2 M ) 2 = B 2 8 μ ,