Two oppositely charged particles moving nonrelativistically in a two-particle Coulomb bound state produce a charge distribution that is equivalent to that of two single-particle bound states of opposite charge moving in separate external potentials. With examples, we show that this is unlikely to be true if the binding force is not pure Coulombic.

1.
For stationary states the two-particle wave function Ψ(r1,r2)=expiP⋅R0ψ(r) in which R0 is the c.m. position and P is the total momentum of the system. The c.m. portion of the wave function will not contribute to the expectation value.
2.
A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1963), Vol. II, p. 815.
3.
H. W.
Crater
and
P.
Van Alstine
, “
Quantum constraint dynamics for two spinless particles under vector interaction
,”
Phys. Rev. D
30
,
2585
–
2594
(
1984
).
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© 1999 American Association of Physics Teachers.
1999
American Association of Physics Teachers
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