Abstract

The problem of emission by an atom is treated according to Schroedinger’s rules. The translational motion of the atom as a whole is taken into account. The charge-current density vector is shown to be propagating with the velocity of light in the direction of the emitted quantum. Only unidirectional quanta can be emitted according to the theory. The reason is that the charge-current wave radiates infinitely more intensely if it travels with light velocity than otherwise.

It is shown that Gordon’s treatment of the Compton effect involves an analogous phenomenon. It is suggested that Schroedinger’s equations designed for the conservation of energy and momentum work out better when the translational motion of the atom as a whole is considered.

© 1927 Optical Society of America

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References

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  1. P. A. M. Dirac, Proc. Roy. Soc.;  111, p. 405; 1926.
    [Crossref]
  2. W. Gordon, ZS. f. Phys.;  40, p. 117; 1926.
    [Crossref]
  3. E. Schroedinger, Ann. d. Physik;  82, p. 257, 1927.
    [Crossref]
  4. E. Schroedinger, Ann. d. Physik,  81, p. 109; 1926.
    [Crossref]
  5. E. Schroedinger, Ann. d. Physik,  82, p. 265; 1927.
    [Crossref]
  6. J. C. Slater, Proc. Nat. Acad. Sci.,  13, p. 7; 1927.
    [Crossref]

1927 (3)

E. Schroedinger, Ann. d. Physik;  82, p. 257, 1927.
[Crossref]

E. Schroedinger, Ann. d. Physik,  82, p. 265; 1927.
[Crossref]

J. C. Slater, Proc. Nat. Acad. Sci.,  13, p. 7; 1927.
[Crossref]

1926 (3)

E. Schroedinger, Ann. d. Physik,  81, p. 109; 1926.
[Crossref]

P. A. M. Dirac, Proc. Roy. Soc.;  111, p. 405; 1926.
[Crossref]

W. Gordon, ZS. f. Phys.;  40, p. 117; 1926.
[Crossref]

Dirac, P. A. M.

P. A. M. Dirac, Proc. Roy. Soc.;  111, p. 405; 1926.
[Crossref]

Gordon, W.

W. Gordon, ZS. f. Phys.;  40, p. 117; 1926.
[Crossref]

Schroedinger, E.

E. Schroedinger, Ann. d. Physik;  82, p. 257, 1927.
[Crossref]

E. Schroedinger, Ann. d. Physik,  82, p. 265; 1927.
[Crossref]

E. Schroedinger, Ann. d. Physik,  81, p. 109; 1926.
[Crossref]

Slater, J. C.

J. C. Slater, Proc. Nat. Acad. Sci.,  13, p. 7; 1927.
[Crossref]

Ann. d. Physik (3)

E. Schroedinger, Ann. d. Physik;  82, p. 257, 1927.
[Crossref]

E. Schroedinger, Ann. d. Physik,  81, p. 109; 1926.
[Crossref]

E. Schroedinger, Ann. d. Physik,  82, p. 265; 1927.
[Crossref]

Proc. Nat. Acad. Sci. (1)

J. C. Slater, Proc. Nat. Acad. Sci.,  13, p. 7; 1927.
[Crossref]

Proc. Roy. Soc. (1)

P. A. M. Dirac, Proc. Roy. Soc.;  111, p. 405; 1926.
[Crossref]

ZS. f. Phys. (1)

W. Gordon, ZS. f. Phys.;  40, p. 117; 1926.
[Crossref]

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Equations (24)

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{ k = 1 3 ( 1 m 2 x k 2 + 1 M 2 X k 2 ) + 8 π 2 h 2 ( E - V ) } ψ = 0
y k = x k - X k ,             ( m + M ) Y k = M X k + m x k
m - 1 = m - 1 + M - 1 ,             M = m + M
{ ( 1 M 2 Y k 2 + 1 m 2 y k 2 ) + 8 π 2 h 2 ( E - V ( y ) ) } ψ = 0
{ 1 m 2 y k 2 + 8 π 2 h 2 ( E - V ) } ψ = 0
ψ = C ( P , n ) ( exp 2 π i h [ ( + E n ) t - ( P Y ) ] ) u n ( y ) = C ( P , n ) e i φ u n ( y )
( P Y ) = P k Y k , P k 2 = 2 M
φ = 2 π h [ ( + E n ) t - ( P Y ) ]
ψ = C e i φ u n ( y ) + C e i φ u n ( y )
e α ψ ψ ¯ d x ,             h e α 4 π i m α ( ψ grad α ψ ¯ - ψ ¯ grad α ψ ) d x
J k = h e 4 π i { - 1 M ( ψ ¯ ψ X k - ψ ψ ¯ X k ) d x + 1 m ( ψ ¯ ψ x k - ψ ψ ¯ x k ) d X }
ρ = e { ψ ψ ¯ d x - ψ ψ ¯ d X }
ψ X 1 = M M ψ Y 1 - ψ y 1 ,             ψ x 1 m M             ψ Y 1 + ψ y 1
4 π i h e J k = 1 M { ( ψ ¯ ψ Y k - ψ ψ ¯ Y k ) d X - ( ψ ¯ ψ Y k - ψ ψ ¯ Y k ) d x } + 1 M ( ψ ¯ ψ y k - ψ ψ ¯ y k ) d x + 1 M ( ψ ¯ ψ y k - ψ ψ ¯ y k ) d x
ψ ψ ¯ = C C ¯ u n 2 + C C ¯ u n 2 + ( C C ¯ e i ( φ - φ ) + C ¯ C e i ( φ - φ ) ) u n u n ψ ¯ ψ Y k - ψ ψ ¯ Y k = - 2 π i h { 2 C C ¯ P k u n 2 + 2 C C ¯ P k u n 2 + ( P k + P k ) ( C ¯ C e i ( φ - φ ) + C C ¯ e i ( φ - φ ) ) u n u n } ψ ¯ ψ y k - ψ ψ ¯ y k = ( u n u n y k - u n u n y k ) ( C C ¯ e i ( φ - φ ) - C ¯ C e i ( φ - φ ) )
1 m g ( y ) G ( Y ) d x + 1 M g ( y ) G ( y ) d X = A g ( y ) G ( Y ) d x - g ( y ) G ( Y ) d X = B
A = g ( z ) { 1 m G ( x 0 + m z M + m ) + 1 M G ( x 0 - M z M + m ) } d z B = g ( z ) { G ( x 0 + m z M + m ) - G ( x 0 - M z M + m ) } d z
A = G ( x 0 ) m g ( z ) d z ;             B = z k ( G ( Y ) Y k ) Y = x 0 g ( z ) d z
ρ = 2 π e i h ( C C ¯ e i ( φ - φ ) - C ¯ C e i ( φ - φ ) ) x 0 u n ( z ) u n ( z ) k = 1 3 z k ( P k - P k ) d z 4 π i h e J k = ( C C ¯ e i ( φ - φ ) - C ¯ C e i ( φ - φ ) ) x 0 { - 4 π 2 M h 2 ( P k + P k ) × ( z k ( P k - P k ) u n u n d z + 1 m ( u n u n y k - u n u n y k ) y = z d z }
φ - φ = 2 π h [ ( + E n - - E n ) t - ( P k - P k ) x k 0 ]
[ φ - φ ] = 2 π h [ ( + E n - - E n ) ( t - r c ) - ( P k - P k - ξ k c ( + E n - - E n ) ) x k 0 ]
P k = P k + ξ k c ( + E n - - E n )
φ - φ = 2 π ν ( t - ξ k x k c )
P k - P k = ξ k c { h ν 0 + 1 2 M l = 1 3 ( P l 2 - P l 2 ) } h ν 0 = E n - E n