a A particle of mass m moves in a threedimensional box with

a.) A particle of mass m moves in a three-dimensional box with sides L. If the particle is in the fourth state i.e. three energy levels above ground state. Find

i.) The energy of the particle

ii.) The combinations of n_x, n_y, n_z that would give this energy

iii.) The wave equations for these different energie states

b.) Determine the quantum numbers l and m_l for the He⁺ ion in the state corresponding to n=3

Solution

b) l=0,1,2

ml=0,(-1,0,1),(-2,-1,0,1,2)