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lambda << 1 must hold and the matrix elements of W are comparable in magnitude to those of H0.

More precisely, the matrix elements of W are of the same magnitude as the difference between the eigenvalues of H0.

I don't understand what is the meaning of " the matrix elements of W are of the same magnitude as the difference between the eigenvalues of H0".

(the above explanation are obtained from the SChaum's Outlines of Quantum Mechanics)