help with number 4

Allantion Problem Set #3 Chem 342 Due: Wed February 19th 1. The wavefunctions for the particle in a 1-D box are given as on ( x ) = 1 1 ( nxx (a) Show that these wavefunctions are eigenfunctions of the Hamiltonian (b) Determine the eigenvalues (c) Show that the wavefunctions are orthogonal 2. Calculate the probability that a particle in a 1-D box of length L is found between 0 and - N/r when described by the following wavefunctions ( a ) 4, ( x ) = 12 s VI sin To. (b ) $2 ( 3* ) = 1 2 sin ( 270 3. For a particle in a 3-D cubic box, what is the degeneracy of the energy level which is a factor of 4 higher than the ground state 4. The uncertainty AA in some observable A can be expressed by AA = V(A) -