申論題

4.(30%) In a one-dimensional energy well with infinite walls as shown below, the wavelength 2 of a particle is limited by the size L of the well with the following relationship: . A. Use de Broglie's wave-particle duality  to show that the allowed energy E of the particle is given by   .B.What is a "zero-point energy"? Why is the zero-point energy necessary according to the Heisenberg Uncertainty Principle? C. If a particle is at the n=4 energy state, what is the probability of finding the particle betweenL?