eigenfunction

An eigenfunction, also known as a proper or characteristic function, is a solution to a differential equation that satisfies specific boundary conditions. In mathematics, particularly in areas like quantum mechanics and linear algebra, eigenfunctions are associated with eigenvalues.123

When a linear operator, represented by P, acts on an eigenfunction, denoted by \u03c8, the result is the same eigenfunction multiplied by a scalar value, known as the eigenvalue, k. This relationship is expressed by the equation P\u03c8 = k\u03c8. Eigenfunctions and their corresponding eigenvalues are crucial for understanding the behavior of systems described by differential equations, such as the Schrödinger equation in quantum mechanics.142