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Hydrogen atom in plane wave electronic field

  1. Nov 29, 2006 #1
    We just consider one dimensional case and the classical method.
    Then the motion equation of the electron in Coulomb field and the plane wave electronic field is
    d^2 x/ dt^2=-1/x^2+cos t. (x is the coordinate and t is the time. )
    How to solve the equation exactly?
    We don't consider such cases as the electron collision with the Hydrogen nucleus.

    Quantum River
  2. jcsd
  3. Nov 29, 2006 #2


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    That's a badly non-linear equation. Do you have any reason to think that it has an exact solution?
  4. Nov 29, 2006 #3
    The equation is a one-body problem. We can't solve the three-body problem, but maybe the one-body problem is always solvable, even if the answer could be highly complex.
    The equation is very useful in physics. So I want to solve it exactly.
    Quantum River
  5. Nov 29, 2006 #4


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    d^2 x/ dt^2=-1/x^2+cos t.

    Are you sure about this equation?

    The left hand side has dimensions of acceleration, while the right-hand side has a mixture of 1/L2 and cos t, which is dimensionless, so the t would have to be mutiplied by 1 (1/T), where T is time.

    if the equation was

    d^2 x/ dt^2=-(cos t)/x^2, then it could be readily solvable, but I doubt it makes physical sense.
  6. Nov 29, 2006 #5
    The part of -1/r^2 actually means the Coulomb force generated by the Hydrogen nucleus.
    The part of cos t is the simplification of e*E0*cos (omega*t).
    e is the electric charge of the particle;
    E0 is the electric field intensity.
    cos t is the change of the electric field.
    Quantum River
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