Consider a particle of mass m in an infinite, one-dimensional, square well potential extending from x = 0 tox= L. The allowed values of the energy, and the corresponding normalised wavefunctions, in the positionrepresentation, are given by E_{n}=\frac{\hbar^{2} \pi^{2}}{2 m L} n^{2} \quad ; \quad\langle x \mid n\rangle=\sqrt{\frac{2}{L}} \sin \left(\frac{\pi x}{L} n\right) Consider the following linear superposition of the ground state and the first excited state: |\psi\rangle=\frac{1}{\sqrt{2}}(|1\rangle-|2\rangle) . What is the position-representation wavefunction, (a)? What is the corresponding probability density? -. What si the expectation value of the position, a? . What is the probability that the particle will be found in the right half of the box, i.e. with L/2 ≤x≤ L?Express your result as a percentage. What is the expectation value of the energy? What is the probability that a measurement of the energy yields the value E₁?