Abstract
The Fredholm determinant of a nonrelativistic Hamiltonian defined on a compact one-dimensional space is evaluated exactly. The Schrödinger equation is rewritten as a first-order differential equation, which is integrated formally. Then a 2 × 2 eigenvalue equation is proved to be proportional to the Fredholm determinant. Our method turns out to be a powerful tool to solve eigenvalue problems in quantum mechanics. Finally several applications of our method are given.
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