A hydrogen molecule in it's ground vibrational state with KE=10eV collides with heavy atom metal surface and no energy is transferred to the surface, i.e., the surface can be modeled as an infinite potential wall. The molecule/surface collision can be modeled as freely moving molecule in 1-D both before and after the collision. The collision is otherwise inelastic so some of the transitional energy is transferred to into higher vibrational states of the molecule. Please look-up the necessary constants and reference your sources. a) Why can the rotational states of the molecule not be considered in this model! b) Before the collision what is the complete Eigen-function of the molecule assuming the surface is located X=0, and V(X?0)=? and V(X>0)=0 and that the molecule is located at a position X>>0, which means the molecule can be treated as a free mass in the region 0>0, the vibrational state (un-normalized) of the molecule is , where |n> are the vibrational Eigen-states, with Eigen-value what is the average vibrational energy of the molecule? d) Using the conservation total of energy between the kinetic and vibrational energy what is the average kinetic energy of the out-going molecule after the collsion? e) Bonus question: what is the complete "wave-function" of the molecule at any point X>0 and what is the complete wave-function for X?0? Explain is would predicted to happen from the total wave function for X>0? Remember this is half of the 1-D square well problem! Email answer to this part of the problem to me separately, ok! It's worth 20 extra points