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Schrödinger's tridiagonal matrix
2021
Special Matrices
In the third part of his famous 1926 paper 'Quantisierung als Eigenwertproblem', Schrödinger came across a certain parametrized family of tridiagonal matrices whose eigenvalues he conjectured. A 1991 paper wrongly suggested that his conjecture is a direct consequence of an 1854 result put forth by Sylvester. Here we recount some of the arguments that led Schrödinger to consider this particular matrix and what might have led to the wrong suggestion. We then give a self-contained elementary
doi:10.1515/spma-2020-0124
fatcat:tmpqvk6aeve7dja5x7nra3edm4