The algebraic eigenvalue problem
The algebraic eigenvalue problem
A First Course in Computational Physics
A First Course in Computational Physics
Numerical Methods for Scientists and Engineers
Numerical Methods for Scientists and Engineers
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Computing in Science and Engineering
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Solutions of the Schrodinger equation that pertain to different energies are orthogonal by virtue of quantum dynamics. However, when we obtain such solutions numerically using library differential equation solvers, and when the inner product is defined by numerical quadrature, the result is not sufficiently orthogonal for certain purposes. This paper shows how to construct stable finite-difference schemes that preserve accurate numerical orthogonality of the solutions.