An eigenfunction is a special type of function that, when acted upon by a linear operator, results in the same function multiplied by a scalar value known as an eigenvalue. This property is crucial in various areas of physics and mathematics, particularly in solving differential equations, as it allows us to simplify complex problems into more manageable parts. Eigenfunctions can be thought of as the 'natural modes' of a system, revealing the inherent characteristics of linear transformations.
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