PHY 4604

Resources — Spring 2013

Materials Shown in Class

Any mention below of a "Physlet" refers to interactive simulations from Physlet® Quantum Physics: An Interactive Introduction by M. Belloni, W. Christian, and A. J. Cox (Pearson Prentice Hall, 2006). Links are provided where available to earlier versions of some simulations that can be accessed for free at the Davidson University Web Physics site.

Links are also provided below to materials that can be accessed under UF subscriptions or license agreements. Generally, you will be able to view these materials if you (1) access them from an on-campus computer, or (2) access them through the UF Libraries proxy tool, or (3) run the Gatorlink VPN software on your computer.

Jan 7 Brief review of complex numbers.
Jan 18 Physlet Section 10.2 implements the "shooting method" for finding spatial wave functions of the infinite square-well potential.
Physlet Section 7.4 implements the shooting method for a particle confined by hard walls to a region in which there is an unknown potential. This situation is quite similar to that in Homework 2, Question 2 (although the specific form of the potential is different).
Jan 25 Physlet Problem 10.6 allows an unknown wave function for the infinite square-well potential to be decomposed to reveal its stationary-state content.
Physlet Problem 10.1 compares the classical and quantum-mechanical probability distributions for a particle in an infinite square-well potential.
Physlet Section 10.6 animates the time evolution of a linear superposition of two low-lying stationary states of the infinite square-well potential.
Research paper "Realization of a particle-in-a-box: Electron in an atomic Pd chain" [N. Nilius, T. M. Wallis, and W. Ho, J. Phys. Chem. B, 109, 20657, (2005)] shows that the low-energy electronic states of a chain of 20 palladium atoms match quite well the predictions of the infinite square-well potential. The paper can be accessed here.
Jan 30 Physlet Section 12.2 shows time-independent solutions of the harmonic oscillator potential for 0 ≤ n ≤ 5.
Physlet Section 12.3 allows direct comparison of the probability densities for classical and quantum-mechanical states of the harmonic oscillator having the same energy En for 0 ≤ n ≤ 5. The classical probability density is that for measurement at a random time during the particle's periodic motion.
Feb 4 Physlet Section 8.4 shows wave functions formed by Fourier summation of plane waves cn exp(iknx) having equally spaced wave vectors kn = k0 + n Δk. In the limit Δk → 0, the Fourier sum becomes a Fourier integral transform.
Feb 6 Notes: The Gaussian wave packet.
Feb 8 Physlet Section 8.6 animates the time-development of a free-particle wave packet.
Pedagogical paper "Continuity conditions on Schrödinger wave functions at discontinuities of the potential [D. Branson, Am. J. Phys. 47, 1000 (1979)] points out flaws in the usual arguments that a one-dimensional wave function ψ(x) and its first derivative must both be continuous across any finite jump in the potential, and provides more rigorous proofs of these conditions. The paper can be accessed here.
Feb 13 Physlet Section 9.4 animates the time-development of stationary states of the step potential.
Physlet Section 9.9 animates the time-development of wave packets incident on a step potential.
Feb 18 Physlet Section 9.6 shows the scattering state ψr(x) vs energy E for a rectangular barrier.
Feb 25 Physlet Section 11.2 illustrates the graphical solution of the conditions satisfied by bound states of a finite square potential well of user-controlled width and depth, and also shows the stationary-state wave functions.
Apr 8 Physlet Section 13.8 plots radial wave functions for the Coulomb potential.
Apr 10 Physlet Section 13.9 represents the full wave functions for the Coulomb potential.

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