# Degeneracy and the Hamiltonian

How many linearly independent eigenfunctions can be associated with one degenerate eigenvalue of the Hamiltonian operator? (Is there a limit since it contains a 2nd order differential operator?) Thanks.

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Do you mean a Hamiltonian in general, or, as your question seems to imply, a Hamiltonian of the form $H = P^2/2m + V(X)$? – Gerben Oct 17 '11 at 12:00