Physics Homework 486: Spring 2007 - Problem Solutions, Assignments of Quantum Physics

Download Physics Homework 486: Spring 2007 - Problem Solutions and more Assignments Quantum Physics in PDF only on Docsity! Physics 486 Spring 2007 Homework #1 1). The wavefunction of an electron confined to a particular potential V(x) is given by ψ(x)=Aexp(-|x|/xo), where A and xo are constants. (a). Sketch this wavefunction. (b). Find the normalization constant A. (c). Calculate the probability that the electron will be measured in the interval –xo<x<xo. (d). Roughly sketch the potential in which the electron is confined (you’ll be surprised!). 2). Consider the potential below, which roughly describes the potential experienced by an electron confined to a quantum well that is in an electric field. (a). Sketch the four lowest bound state wavefunctions for this potential; pay particular attention to the amplitude and curvature of the wavefunction in and out of the well. (b). Consider the 3rd energy level. Qualitatively, where is the electron most likely to be observed? Please justify your answer. (c). Without trying to solve the Schrödinger equation for this potential, explain how the allowed energies for the electron in this potential will compare to those of the finite square well potential. Be as detailed as possible, and provide your reasoning. 3). In this problem, you will use the one-dimensional infinite square well (ISW) potential to make simple estimates of physically relevant parameters. (a). Using the ISW potential as a model of the hydrogen atom, and the fact that the Lyman α radiation (n=2 to n=1) has a wavelength λ = 1216.0 Å, to estimate the diameter of the hydrogen atom. How does your value compare with twice the Bohr radius? (b). Suppose that the potential seen by a neutron confined to the nucleus can be represented in one-dimension by an ISW potential of width 10-12 cm. Estimate the lowest energy of the neutron in the nucleus. x V(x) x = 0 V = 0 x = L Vo V(x) ~ eEx