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.
JP.C. Mbagwu, B.I. Madububa, J.O. Ozuomba and M.C. Udoye, 2021. Series Solutions of Mathematical Problems of Quantum Mechanics. Research Journal of Applied Sciences, 16: 204-211.