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Miloslav Znojil (Nuclear Physics Institute AS CR, Rez, Czech Republic)
Zeros of classical orthogonal polynomials as eigenvalues of quantum observables
Abstract:
A new form of applicability of classical orthogonal polynomials
Cn(x) is quantum theory is proposed. The key idea of the
proposal is that whenever CN(xN)=0, the truncated form of
the standard three-term recurrences satisfied by the set of
polynomials Cn(xN) with n=0, 1, ..., N-1 may be
re-read as a non-Hermitian-matrix eigenvalue problem which admits
N alternative isospectral Hermitizations. The main mathematical
ingredient of our proposal is revealed to lie in the feasibility of
an exhaustive and constructive, closed-form enumeration and partial
ordering of these Hermitizations.
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