1. The wave function for a free particle is Y(x, t) = exp[i(kx-cot)] (where k is the wave vector, x is the position, w is the angular frequency and t is the time). For each of the following operators, determine if the wavefunction is an eigenfunction of that operator. If it is an eigenfunction, compute the eigenvalue and if not compute the expectation value. a. Hamiltonian operator: Ĥ== 2m ax² b. Momentum operator: p=4& c. Position operator: x= x d. Energy operator: Ê-d

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