Z-component of the angular momentum is conserved. Similarly, translation symmetry gives rise to conservation of linear momentum, inversion symmetry gives rise Molecular symmetry in physics and chemistry describes the symmetry present in molecules and the classification of molecules according to their symmetry. Molecular symmetry is a fundamental concept in the application of quantum mechanics in physics and chemistry, for example, it can be used to predict or explain many of a molecule's properties, such as its dipole moment and its allowed spectroscopi Some specific examples can be systems having rotational, translational invariance etc. For a rotationally invariant system, the symmetry group of the Hamiltonian is the general rotation group. Now, if (say) the system is invariant about any rotation about Z-axis (i.e., the system has axial symmetry), then the symmetry group of the Hamiltonian is the group of rotation about the symmetry axis. Now, this group is generated by the Z-component of the orbital angular momentum, L z {\displaystyle {L}_{z}} (general group element R ( α ) = e − i α L z ℏ {\displaystyle R(\alpha )={{e}^{\frac {-i\alpha {{L}_{z}}}{\hbar }}}} ). Thus, L z {\displaystyle {L}_{z}} commutes with H {\displaystyle H} for this system and Z-component of the angular momentum is conserved. Similarly, translation symmetry gives rise to conservation of linear momentum, inversion symmetry gives rise to parity conservation and so on.