Summary: We prove that the wave operators for \(n \times n\) matrix Schrödinger equations on the half line, with general selfadjoint boundary condition, are bounded in the spaces \(L^p (\mathbb{R}^+, \mathbb{C}^n)\), \( 1 < p < \infty\), for slowly decaying selfadjoint matrix potentials \(V\) that satisfy the condition \(\int_0^{{\infty}} (1 + x) |V (x)| \,d x < {\infty}\). Moreover, assuming that \(\int_0^{{\infty}} (1 + x^\gamma) |V (x)|\,d x < {\infty}\), \(\gamma > \frac{5}{2}\), and that the scattering matrix is the identity at zero and infinite energy, we prove that the wave operators are bounded in \(L^1 (\mathbb{R}^+, \mathbb{C}^n)\) and in \(L^{{\infty}} (\mathbb{R}^+, \mathbb{C}^n)\). We also prove that the wave operators for \(n \times n\) matrix Schrödinger equations on the line are bounded in the spaces \(L^p (\mathbb{R}, \mathbb{C}^n)\), \(1 < p < {\infty}\), assuming that the perturbation consists of a point interaction at the origin and of a potential \(\mathcal{V}\) that satisfies the condition \(\int_{-\infty}^{\infty} (1+|x|)|\mathcal{V}(x)|\, dx<\infty\). Further, assuming that \(\int_{-\infty}^{\infty} (1+|x|^\gamma)|\mathcal{V}(x)| \,dx<\infty\), \(\gamma > \frac{5}{2}\), and that the scattering matrix is the identity at zero and infinite energy, we prove that the wave operators are bounded in \(L^1 (\mathbb{R}, \mathbb{C}^n)\) and in \(L^{{\infty}} (\mathbb{R}, \mathbb{C}^n)\). We obtain our results for \(n \times n\) matrix Schrödinger equations on the line from the results for \(2 n \times 2 n\) matrix Schrödinger equations on the half line.

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