All Problems Wave Properties of particles. Schrodinger Equation.
Problem 6.83
A particle of mass \(m\) is located in a three-dimensional cubic potential well with absolutely impenetrable walls. The side of the cube is equal to \(a .\) Find: (a) the proper values of energy of the particle; (b) the energy difference between the third and fourth levels; (c) the energy of the sixth level and the number of states (the degree of degeneracy) corresponding to that level.
6.83. (a) \(\dot{E}=\left(n_{1}^{2}+n_{2}^{2}+n_{3}^{2}\right) \pi^{2} \hbar^{2} / 2 m a^{2},\) where \(n_{1}, n_{2}, n_{3}\) are integers not equal to zero: (b) \(\Delta E=\pi^{2} \hbar^{2} / m a^{2} ;\) (c) for the 6-th level \(n_{1}^{2}+n_{2}^{2}+n_{3}^{2}=14\) and \(E=7 \pi^{2} \hbar^{2} / m a^{2} ;\) the number of states is equal o six (it is equal to the number of permutations of a triad \(1,2,3 .)\)