Abstract: Quantum mechanics has played a major role in photonics, quantum electronics, and microelectronics. A series method is a powerful tool for solving quantum mechanical problems. In this study, we obtained the approximate solutions of operators using Harmonic Oscillator in a linear combination of the energy eigenstates. Also, the commutator of monomials of operators obeying constant commutation relations is expressed in terms of anti-commutators. We obtained the angular momentum operators in an eigenfunction with the use of matrices. Finally, we determined some exact solutions of eigenvalues and eigenvectors in a matrix representation of the operator to some set of orthonormal basis vectors.