The Determination of Eigenvalues and Eigenvectors of the Orbital Angular Momentum

Abstract

The theory of angular momentum performance a significant position in the classical and quantum mechanical study of physical properties, such as studies into nuclear, atomic, and molecular processes, as well as other quantum problems, including spherical symmetry. In this analysis, angular momentum operators are described in multiple ways, based on the angular momentum operator's commutator, matrix, and geometric representation, The eigenvalue and eigenvector were also known for operatorsJ ̂_±,J ⃑ ̂^2, J ̂_x,J ̂_y and J ̂_zwithin the |j,┤ ├ m⟩ basis. Furthermore, in quantum mechanics, angular momentum is called quantized variable, meaning that it comes in discrete quantities. In contrast to the macroscopic system case where a continuous variable is angular momentum.

Keywords

• Orbital angular momentum
• Quantization
• Raising and lowering operators
• Quantum numbers
• Matrix and graphical representation

References

1. 1. Zettili, N., Quantum mechanics: concepts and applications. 2003, American Association of Physics Teachers.
2. 2. Griffiths, D.J. and D.F. Schroeter, Introduction to quantum mechanics. 2018: Cambridge University Press.
3. 3. Cohen-Tannoudji, C., B. Diu, and F. Laloe, Quantum Mechanics, vol. 1, 231. 2005, Singapore: Wiley.