PH 253 Final: ph253_S10_FINAL_soln
Document Summary
The wavefunction for a particle in a 1d box may be written. (x) = a sin bnx (1) where a and b are constants you will need to nd, and n is an integer. Our boundary conditions are that the wavefunction vanish at the boundaries of the box x = 0 and x = l, since the potential is in nite outside of that region. i. Thus, (x) = a sin(cid:0) n x enforcing normalization (i. e. , the probability density integrated over all space must give unity). Since the wavefunction vanishes outside [0, l], we need only integrate over that interval. We need only determine the overall constant a, which can be done by. 2(cid:19) (1 cos 2u) du (cid:16)let u = n x. For the ground state, n = 1, and p = 1. 2 0. 091: the wave function for the ground state of hydrogen (n = 1) is e r/ao.
