In quantum mechanics, a wave function (ψ) describes the state of a particle and contains all information about its position, energy, and behavior. When an operator (such as the energy or momentum operator) acts on a wave function and returns the same function multiplied by a constant, that function is an eigenfunction, and the constant is the eigenvalue.
Eigenvalues represent measurable physical quantities—like energy levels—while eigenfunctions describe the allowed states of a quantum system. These concepts are central to solving the Schrödinger equation and understanding quantized energy levels.
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