In the system for which they are most often used, these can be derived from the commutator of two different components of the associated operator, which is plus or minus i times h-bar times the third component.
The commutator of a given operator that has an associated one of these returns the original operator scaled by a constant. These map the associated operator's eigenfunctions onto itself, though they may have no eigenfunctions themselves. Solving problems using them is called the algebraic method. The matrix elements of these objects are zero except that they have quantities proportional to the square roots of the natural numbers on the diagonal above or below the main diagonal. In the system for which they are most often used, these can be derived from the commutator of two different components of the associated operator, which is plus or minus i times h-bar times the third component. In that same system, applying one of these repeatedly allows one to show that the system has a ground-state energy of half h times the frequency. Usually constructed for the angular momentum operator for a quantum harmonic oscillator, for 10 points, name these operators that cause an eigenvalue to increase or decrease by one unit.
The commutator of a given operator that has an associated one of these returns the original operator scaled by a constant.
angular momentum ladder operators [or creation and annihilation operators; or raising and lowering operators; or promotion and demotion operators]