Show that the wavefunction y = eikx + e-ikx is an eigenfunction of the hamiltonian operator for a free particle (for which potential energy, v, = 0 everywhere). normalization of wavefunctions 3. consider the function from question 1 (e-ax). based on the condition that wavefunctions of physical systems must be normalizable, is this an acceptable wavefunction? 4. find the normalization factor for the wavefunction y(x) = eix for x = -0.5 to 0.5. 5. let's suppose i confine the particle i'm interested in to x values between zero and some distance a. (meaning that the particle must exist somewhere between 0 and a.) find the normalization factor and write out the normalized wavefunctionf for: w(x) = sin (ex); where a is a constant note: totally fine with me if you use something like wolframalpha to evaluate this, but if you do, screenshot your input and result to submit to me.