Eigenvalue and eigenfunction are mathematical concepts used in linear algebra and quantum mechanics. An eigenfunction of a linear operator is any non-zero function in that space that, when acted upon by the operator, is only multiplied by some scaling factor called an eigenvalue. In other words, an eigenfunction is a type of eigenvector. In quantum mechanics, the wave function of a particle is an eigenfunction of the Hamiltonian operator, which represents the total energy of the particle/03%3A_The_Schrodinger_Equation/3.04%3A_Operators%2C_Eigenfunctions%2C_Eigenvalues%2C_and_Eigenstates). The eigenvalue represents the energy of the particle in that state. When a system is in an eigenstate of an observable, the expectation value of that observable is the eigenvalue of the wave function/21%3A_Operators_and_Mathematical_Background/21.02%3A_Eigenfunctions_and_Eigenvalues). The concept of eigenfunctions and eigenvalues is also used in solving boundary value problems in differential equations.