A6. Suppose that the wavefunction for a particle, constrained to exist between 0 < x < 1, is given by (x) = B(x – x2), where B is a constant. Assume that the wavefunction vanishes outside the allowed region. (a) Sketch the wavefunction, and show clearly how it satisfies the continuity/smoothness con- ditions required by the Schrödinger equation. (b) What is the probability of finding the particle in the left-hand third of this well? (c) Find the expectation values of x and x2. (d) Determine the uncertainty of the particle's position.

A6. Suppose that the wavefunction for a particle, constrained to exist between 0 < x < 1, is given by (x) = B(x – x2), where B is a constant. Assume that the wavefunction vanishes outside the allowed region. (a) Sketch the wavefunction, and show clearly how it satisfies the continuity/smoothness con- ditions required by the Schrödinger equation. (b) What is the probability of finding the particle in the left-hand third of this well? (c) Find the expectation values of x and x2. (d) Determine the uncertainty of the particle's position.