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Asymptotic boundary condition, incoming

Thus A + ) has the outgoing boundary condition while A ) has the incoming boundary condition and they are called scattered waves. From Eqs. (63-67), the asymptotic boundary conditions for (A ) are... [Pg.248]

Equ. (7.20) describes for an out -state the asymptotic behaviour of the stationary wavefunction. As discussed above, the characteristic property of this state is that the incoming spherical waves e Kr/r have the scattering amplitude /(-)( ). It is this minus sign in the exponential term of the incoming spherical waves which is kept as a superscript to characterize the out -state, and the relation described by equ. (7.20) is frequently called the incoming spherical waves boundary condition. Hence, one should not mix up the state with the waves. [Pg.285]

Remembering the phase factor e ia>t, this relation expresses quantitatively the result which was used above, i.e. a plane wave can be described asymptotically as a sum of undisturbed outgoing and incoming spherical waves, which differ only in their relative phases. The boundary condition of equ. (7.20) can then be expressed as... [Pg.287]

If the limit is negative, then the channel is closed and the nuclei remain bounded to each other. The form of the solutions of the coupled equations, Eqs. (39 or 40), depends on the imposed boundary conditions. Consider first the case where there is at least one open channel. Scattering boundary conditions consist of imposing, for an open channel n, a combination of incoming (exp [ - ik R]) and outgoing (exp [ - - iknR]) waves, while all closed channel functions are constrained to vanish asymptotically. In the case... [Pg.69]

The first part yields asymptotically the plane incoming wave, the second the outgoing spherical wave. So by (42) we have satisfied all boundary conditions. [Pg.49]

By comparison of the coefficients with the asymptotic representation of the incoming plane wave by Hankel functions we obtain from boundary condition I for... [Pg.53]


See other pages where Asymptotic boundary condition, incoming is mentioned: [Pg.247]    [Pg.211]    [Pg.22]    [Pg.2295]    [Pg.214]    [Pg.19]    [Pg.70]    [Pg.174]    [Pg.55]    [Pg.98]    [Pg.117]    [Pg.196]    [Pg.196]   
See also in sourсe #XX -- [ Pg.247 ]




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