On the Non-Orthonormality of Lippmann-Schwinger-Low States

Details On the Non-Orthonormality of Lippmann-Schwinger-Low States On the Non-Orthonormality of Lippmann-Schwinger-Low States

2000-02-15

arxiv.org/abs/quant-ph/0002042v2

Physics

Quantum Physics

9 pages (modified version)

Scientific paper

It is pointed out that for a general short-ranged potential the Lippmann-Schwinger-Low scattering state $|\psi^L_k>$ does not strictly satisfy the Schrodinger eigen equation, and the pair $|\psi^L_n>$, $|\psi^L_k>$ is mutually nonorthogonal if $E_n=E_k$. For this purpose, we carefully use an infinitesimal adiabatic parameter $\epsilon$, a nonlinear relation among transition amplitudes, and a separable interaction as illustration.

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