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.

Lease Defaults and the Efficient Mitigation of Damages

The traditional law of leases imposed no duty on landlords to mitigate damages in the event of tenant breach, whereas the modern law of leases does. An economic model of leases, in which absentee tenants may or may not intend to breach, shows that the traditional rule promotes tenant investment in the property by discouraging landlord entry. In contrast, the modern rule prevents the property from being left idle by encouraging landlords to enter and re-let abandoned property. The model reflects the historic use of the traditional rule for agricultural leases, where absentee use was valuable, and the emergence of the modern rule for residential leases, where the primary use entails continuous occupation.

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.

Contractual Difficulties in Environmental Management and the Protection of Biodiversity: The Case of Conservation and Mitigation Banking

This paper offers a principal-agent model of feasible private contracting in mitigation and conservation banking aimed at the protection of natural habitat and bio-diversity of US wetlands and uplands. It is shown that while it is straightforward to design an incentive contract, such a contract may not achieve the federally mandated objective of no net loss of habitat. This is because the minimum payment required as an economic incentive to private agents may be greater than what they should receive for the habitat values that they actually created in the field. This possible problem is shown to derive from nonconvexity in the production possibility set between the biological value of land as natural habitat and in non-habitat uses such as in urban development. The paper concludes with a consideration of several institutional devises that may promote the convergence of private contracting and the attainment of no net loss. These include the payment of subsidies, greater accuracy in the identification of actual quality by the principal, and the use of several incentive alignment devises.

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.