Abstract
A method is proposed for obtaining the eigenvalues and eigenfunctions of the one-dimensional time-independent Schrodinger equation. The eigenvalue problem is transformed into a system of two first-order ordinary linear differential equations. The propagation matrix for the solution is written as the exponential of a traceless matrix which is then approximated by the Magnus expansion. The bound-state eigenvalues and eigenfunctions are obtained by requiring that the latter satisfy the appropriate boundary conditions. The Morse potential is considered as an illustrative example.
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