The Harmonic Oscillator, a Review of Classical and Elementary Quantum Mechanics

The classical harmonic oscillator and an elementary discussion of the quantum mechanical solutions for the harmonic oscillator are discussed.

Guessing Harmonic Oscillator Wavefunctions Using Maple

The guessing of eigenfunctions is not trivial at higher quantum numbers, no matter what the system being considered. Instead of guessing, one can employ a symbolic calculus progam (Maple in this case) to aid in the reasoning process.

The Harmonic Oscillator's Frobenius Solution

The Frobenius solution to the differential equations associated with the harmonic oscillator (QM) is carried out in detail.

Advance P. Chem. Problems (I) Populations, Partition Functions, Particle in Box, Harmonic Oscillators, Angular Momentum and Rigid Rotor

This is a set of P. Chem. problems posed at slightly higher than the normal text book level, for students who are continuing in the study of this subject.

The Driven Harmonic Oscillator in Chemistry

The molecular dynamical simulation of the normal vibrational mode of water which involves H-O-H angle deformation, when driven by an external force, can be used to see how a driven harmonic oscillator, classically, is associated with the infra-red spectrum of water (and the absorption for this particular normal mode).

Molecular Dynamics and the Diatomic Molecule as Harmonic Oscillator and Rigid Rotor

The HCl molecule is simulated (using Maple) in its dynamics, for both vibrational (and implied) rotational motions. A discussion of the center of mass transformations involved is part of the total presentation.

Emissions Control and the Regulation of Product Markets: The Case of Automobiles

The paper investigates alternative policies to regulate emissions from polluting product markets, specifically considering the case of the automobiles market. The two policies we consider are: a quota that limits the quantity produced of the polluting model and a more flexible average efficiency standard that requires a minimum energy efficiency across all models produced by a firm, similar to the US Corporate Average Fuel Economy (CAFE) standards. We use a duopoly model of vertical differentiation where firms produce both an economy (i.e., low polluting) version and a luxury (i.e., high polluting) version of a given product. We show that while a quota can raise firm profit over a certain range, CAFE always reduces firm profit relative to the pre-regulation. We also show that while the quota reduces emissions, it is possible that emissions increase under CAFE. The optimal policy choice will depend on the magnitude of unit damages. We show that when unit damages are sufficiently high, the quota policy is more efficient than the average efficiency standard. This suggests that instead of tightening CAFE to limit damages from emissions, policy makers can shift to a quota policy which is both welfare enhancing and more profitable for firms.