Frank Rioux

Calculating diffraction patterns

Following Marcella’s approach to the double-slit experiment (Marcella T V 2002 Eur. J. Phys. 23 615–21), diffraction patterns for two-dimensional masks are calculated by Fourier transform of the Mask geometry into momentum space. Iw ish to describe a simple extension of Marcella’s [1] recent analysis of the double-slit experiment to two dimensions. The essential point Marcella makes in his unique treatment of this well-known experiment is that the diffraction pattern at the detection screen is actually a measurement of the momentum distribution of the diffracted particles. Therefore the calculate dd iffraction pattern is simply obtained from the Fourier transform of the coordinate space wavefunction (the doubleslit geometry) into momentum space. Marcella considered two spatial models: (model 1) infinitesimally thin slits represented by Dirac delta functions; and (model 2) slits of finite width. About 60 years ago Sir Lawrence Bragg [2] proposed the optical transform as an aid in the interpretation of the x-ray diffraction patterns of crystals. This required the fabrication of two-dimensional masks of various crystal or molecular geometries and the generation of the diffraction pattern using visible electromagnetic radiation. Present-day laser technology has made the generation of suc hd iffraction patterns routine, even in the classroom. In addition, Marcella’s computational approach makes calculating the diffraction patterns conceptually and mathematically straightforward. If one considers the mask as consisting of point scatterers (model 1), the coordinate space wavefunction is a linear superposition of the scattering positions: |� �= 1 √ N

A Hartree self-consistent field calculation on the helium atom

The paper presents a simple numerical Hartree self-consistent field calculation for the helium atom. It is intended for use with undergraduate students in introductory courses on quantum mechanics.

Charge cloud study of atomic and molecular structure

The conceptually simple charge cloud model of atomic and molecular structure is applied to three problems: atomic hydrogen, molecular hydrogen, and crystalline lithium hydride. Because of its simplicity, the model lends itself well to calculations that are easily performed by undergraduates. While the calculations are, on the whole, only in modest agreement with experimental results, the model provides useful insights in all the areas to which it is applied.

A simple self-consistent-field calculation for two-electron systems

Presents a simple illustration of an analytical self-consistent-field calculation for two-electron atoms or ions. The calculation is mathematically straightforward and clearly reveals the essential elements of the self-consistent-field method. It might serve as an introduction to the more comprehensive treatments to be found in the chemical physics literature.

Self‐consistent‐field calculation on lithium hydride for undergraduates

Students generally acquire an understanding of theoretical concepts only after they have attempted actual calculations based on those concepts. Consequently there is a need for realistic calculations in quantum theory which can be used with undergraduates to illustrate its important concepts. In this paper we describe a self‐consistent‐field–linear combination of atomic ortibals–molecular orbital calculation on the valence electrons of LiH using the method of Roothaan. The calculation is modest in scope, mathematically simple, and easy to program. These factors enhance its usefullness with undergraduates.

Response to Potential-Energy-Only Models

Commentary on the suitability of the potential-energy-only (POE) model for explaining successive ionization energies.

A Comment on the Energy Levels of the Lithium atom

Recently Saleh-Jahromi and Moebs (1998 Eur. J. Phys. 19 355) presented an interesting set of calculations on two-electron (He, , ) and three-electron (Li, , ) species suitable for undergraduate quantum mechanics courses. This comment offers an extension to these calculations on the three-electron species.

Kinetic Energy and the Covalent Bond in H2

A modified version of Ruedenberg’s innovative analysis of the chemical bond in the hydrogen molecule ion is presented that factors the bond energy into bonding and nonbonding contributions. This simplified approach clearly illustrates Ruedenberg’s main thesis: chemical bond formation is driven by a decrease in electron kinetic energy.

Series solutions and the variational principle

The B matrix method of Frost for solution of nonseparable Schrodinger equations is used in combination with the upper bound theorem for linear variation functions to show that series solutions are possible in the general case without explicit evaluation of integrals. The procedures are illustrated with calculations on the hydrogen‐molecule ion, with some discussion of the helium atom.