According to the Bohr-Sommerfeld postulate the periodic motion of a particle in a potential field must satisfy the following quantization rule: where q and p are generalized coordinate and momentum of the particle,
n are integers. Making use of this rule, find the permitted values of energy for a particle of mass m moving
(a) In a unidimensional rectangular potential well of width l with infinitely high walls;
(b) Along a circle of radius r;
(c) In a unidimensional potential field U =ax2/2, where α is a positive constant;
(d) Along a round orbit in a central field, where the potential energy of the particle is equal to U = â a/r α is a positive constant).