If the operator acts on a function equal to the constant g multiplied by the function, the equation is called an eigenequation.

This function is called the eigenfunction of the operator, and g is the eigenvalue of the operator corresponding to the eigenfunction.

Many problems in quantum mechanics are to find out the eigenvalue and eigenfunction of the mechanical quantity operator of the system by solving the eigenequation, so as to determine various possible values of the mechanical quantity of the system; On the other hand, eigenvalues are often discrete and discontinuous (mathematically, they are often caused by the finite boundary conditions of definite solutions), which reflects the discrete phenomenon in quantum mechanics from another angle.

For example, the stationary Schrodinger equation is essentially the eigenvalue equation of the energy operator, and energy is its eigenvalue. For quantum steady-state problems, finite boundary conditions often lead to finite and discrete eigenvalues, which is the discontinuity of energy classification under the microscope.