Optical potential so far, we assumed that the potential v(x) is real. since the schrödinger equation is already complex, we can ask what happens if we add an imaginary term to it-this is called an 'optical potential'. in class, you derived that the total probability always satisfies p(t)0. evaluate this derivative again, but without assuming that v(x) is real. you will see that it doesn't vanish anymore. now assume that the imaginary part of v(x) is a constant -vo. find a differential equation for p(t). assuming that p(o) 1, solve it to find p(t) in terms of vo and note: we will not use this in the rest of this class, but you will see it again in nuclear physics, where it's used to model particles that can be absorbed or decay. can you see why?

The bubba chump shrimp company processes and packages shrimp for sale to wholesale seafood distributors. the shrimp are transported to the main plant by trucks that carry 1,000 pounds (lb) of shrimp. once the continuous flow processing of the shrimp begins, no inventory is allowed in buffers due to spoilage and all of the shrimp must be processed within 12 hours to prevent spoilage. the processing begins at the sorter, where the trucks dump the shrimp onto a conveyor belt that feeds into the sorter, which can sort up to 500 lb per hour. the shrimp then proceed to the desheller, which can process shrimp at the rate of 400 lb per hour. however, after 3 hours and 45 minutes of processing, the desheller must be stopped for 15 minutes to clean out empty shrimp shells that have accumulated. the veins of the shrimp are then removed in the deveining area at a maximum rate of 360 lb per hour. the shrimp proceed to the washing area, where they are processed at 750 lb per hour. finally, the shrimp are packaged and frozen. what is the daily process capacity of the processing plant (excluding the packaging and freezing)?