An electron is described by the 1D wave function: 0 for33 0 where a is a real constant with dimensions in1 (i) What is the probability of nding the particle at some specic 9: for x 0? Why? (iii) Around what value of ac is the probability of nding an electron the highest? Why? What role does the probability density play versus probability here? Calculate the relevant position and give your answer in terms of 1/a. Hint: bear in mind that came\" = (3(""+b)'c and treat the problem like you would any other quadratic equation. (iv) Calculate the expectation value (as) of measurements of position performed on an ensemble of identically prepared particles. (v) Explain why the results of parts (c) and (d) are different. (vi) Is this wave function for the electron an eigenfunction of momentum? Give your reason