Particle in an infinite square well
A particle moving on the x axis is confined to a onedimensional box of edge length L with one end at the origin and the other at x=L. The confining potential seen by the particle vanishes inside the box, and is infinite outside the box; the appropriate boundary condition is that ϕ(x) vanish at the edges and outside the box. Solve the energy eigenvalue equation for this system in the region inside the box to obtain a set of appropriately normalized energy eigenfunctions and eigenvalues. Are the energy eigenfunctions for this system also eigenstates of the component of the momentum operator P_x = i hbar partial derivative with respect to x?
I believe I have the correct solution to the energy operator, but I am not totally sure of my answer that the momentum operator is not an eigenstate of the momentum operator. Could someone please check the momentum operator part of question 7? Problem set and answer sheet are attached.
Thank you.
