8. Background information needed to answer the next question: A fundamental property of waves is their ability to add together to form complex wave patterns. This property can be observed in a swimming pool where many waves from different people splashing in the water superimpose to form the complex ripples that are observed on its surface. The wave nature of electrons in atoms allows multiple wavefunctions to superimpose as well. These are called superposition states. For example, a hydrogen atom in its ground state has one electron in a 1s hydrogenic orbital. However, placement of the atom in a strong electric field oriented along the x-axis causes the ground state of the atom to become a superposition of a 1s and 2px hydrogenic orbital =0.9541s+0.32px. In this expression, the coefficients in front of the hydrogenic orbitals describe the contribution each makes to the total superposition. The wavefunction of the superposition state has been normalized such that 2d=1. Question 8): (15 points) Determine whether the super position state =0.9541s+0.32pz is an eigenfunction of the l^z operator. If it is, give the eigenvalue. If not, then calculate the expectation value for lz. Explicitly evaluate all eigenvalue equations and/or integrals and simplify your answer to a number multiplied by