A1-d harmonic oscillator is prepared in a superposition of its ground state and its second excited state, with wavefunction where ψ0(x) and 2(x) are eigenfunctions of the hamiltonian with energy fo and 5e0 (a) let a and at denote the oscillator ladder operators. determine the wavefunctions that result from the following operations: àl/(x), à2> (x), 2), and ààub(x). (b) the oscillator has mass m and frequency w. evaluate the expectations () and where is the position operator (c) the oscillator evolves freely for a time t. what is the wavefunction at time t?