outside the interval [0,1]

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11: 18.39 Applications in the Physical Sciences

… ►where the orthogonality measure is now $dr$, $r\in [0,\mathrm{\infty }).$ … ►Orthogonality, with measure $dr$ for $r\in [0,\mathrm{\infty })$, for fixed $l$ … ►which maps $ϵ\in [0,\mathrm{\infty })$ onto $x\in [-1,1]$. … ►For $Z>0$ these are the repulsive CP OP’s with $x\in [-1,1]$ corresponding to the continuous spectrum of $\mathscr{H}(Z)$, $ϵ\in (0,\mathrm{\infty })$, and for we have the attractive CP OP’s, where the spectrum is complemented by the infinite set of bound state eigenvalues for fixed $l$. … ►For either sign of $Z$, and $s$ chosen such that $n+l+1+(2Z/s)>0$, $n=0,1,2,\mathrm{\dots }$, truncation of the basis to $N$ terms, with $x_i^N\in [-1,1]$, the discrete eigenvectors are the orthonormal $L^2$ functions …