Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Scientific Computing
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We present a numerically precise treatment of the Crank-Nicolson method with an imaginary time evolution operator in order to solve the Schrodinger equation. The time evolution technique is applied to the inverse-iteration method that provides a systematic way to calculate not only eigenvalues of the ground-state but also of the excited-states. This method systematically produces eigenvalues with the accuracy of eleven digits when the Cornell potential is used. An absolute error estimation technique is implemented based on a power counting rule. This method is examined on exactly solvable problems and produces the numerical accuracy down to 10^-^1^1.