Problem 3.16 Show that two noncommuting operators cannot have a complete set of common eigenfunctions. Hint: Show that if ê and Ö have a complete set of common eigenfunctions, then P, Qf = 0 for function in Hilbert space.

It's a quantum mechanics question.

A particle of mass 1.60 x 10-28 kg is confined to a one-dimensional box of length 1.90 x 10-10 m. For n = 1, answer the following. (a) What is the wavelength (in m) of the wave function for the particle? m (b) What is its ground-state energy (in eV)? eV (c) What If? Suppose there is a second box. What would be the length L (in m) for this box if the energy for a particle in the n = 5 state of this box is the same as the ground-state energy found for the first box in part (b)? m (d) What would be the wavelength (in m) of the wave function for the particle in that case? m

It's a quantum mechanics question.