1. Let's say you have a particle of mass m in a 1D potential given by V(x) = a + bx2, where a and b are constants. (a) (5 pts) What are the eigenenergies of this system? (b) The particle has a wavefunction given by an equal-weight superposition of the ground and first excited states at time t = 0 (Make sure to define all the symbols you use in terms of the constants a and b given in the problem). i. (10 pts) What is the expected position of the particle at t > 0? ii. (10 pts) What is the expected potential energy at time t > 0? iii. (5 pts) What is the expected value of total energy at time t > 0