We present numerically exact solutions of the time-independent Schrödinger equation for the following system: two particles of the same charge, repelled by the Coulomb force, confined to a one-dimensional infinite well. The eigenfunctions are expanded in a basis set of product delta functions; the expansion allows the removal of the Coulomb potential’s singularity. We report and discuss our findings regarding correlated behavior in the lowest energy states of a well of length 3 bohr (1 bohr=1 Bohr radius≈0.52 Å).
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Lowest eigenvalues for and bohr: and with exact values of last digits shown in parentheses. Full diagonalization of a 300×300 matrix by a general routine should take less than 10 min on a small computer.
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© 2001 American Association of Physics Teachers.
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