Abstract
A first-order variational principle for a stationary scattering phase is obtained by keeping constant the energy normalization for permitted variations of the wave function. The principle is used to derive (i) a variational correction to the phase obtained from given approximate wave functions, (ii) a first-order perturbation theory, (iii) a first Born approximation and (iv) a variational method for obtaining approximate wave functions analogous to that of Kohn. (i), (ii) and (iii) are more generally applicable than the corresponding expressions for tan δl and sin δl, where δl is the phase, and simple models suggest that they are more accurate than for tan δl, but an example indicates that (iv) may be worse than Kohn's variational method. A possible explanation is given. The theory is generalized to many channels. Many complications arise which are absent or trivial for one channel, and the generalization is not complete, since we are unable to define a stationary phase matrix, and the range of application is more limited.
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