A simple, rigorous geometrical representation for the Schrodinger equation is developed to describe the behavior of an ensemble of two quantum‐level, noninteracting systems which are under the influence of a perturbation. In this case the Schrodinger equation may be written, after a suitable transformation, in the form of the real three‐dimensional vector equation dr/dt=ω×r, where the components of the vector r uniquely determine ψ of a given system and the components of ω represent the perturbation. When magnetic interaction with a spin ½ system is under consideration, ``r'' space reduces to physical space. By analogy the techniques developed for analyzing the magnetic resonance precession model can be adapted for use in any two‐level problems. The quantum‐mechanical behavior of the state of a system under various different conditions is easily visualized by simply observing how r varies under the action of different types of ω. Such a picture can be used to advantage in analyzing various MASER‐type devi...

Geometrical Representation of the Schrödinger Equation for Solving Maser Problems

*1. The Discovery of Deep Time * Deep Time * Myths of Deep Time * On Dichotomy * Time's Arrow and Time's Cycle * Caveats *2. Thomas Burnet's Battleground of Time * Burner's Frontispiece * The Burnet of Textbooks * Science versus Religion? * Burnet's Methodology * The Physics of History * Time's Arrow, Time's Cycle: Conflict and Resolution * Burnet and Steno as Intellectual Partners in the Light of Time's Arrow and Time's Cycle *3. James Hutton's Theory of the Earth: A Machine without a History * Picturing the Abyss of Time * Hutton's World Machine and the Provision of Deep Time * The Hutton of Legend * Hutton Disproves His Legend * The Sources of Necessary Cyclicity * Hutton's Paradox: Or, Why the Discoverer of Deep Time Denied History * Borges's Dilemma and Hutton's Motto * Playfair: A Boswell with a Difference * A Word in Conclusion and Prospect *4. Charles Lyell, Historian of Time's Cycle * The Case of Professor Ichthyosaurus * Charles Lyell, Self-Made in Cardboard * Lyell's Rhetorical Triumph: The Miscasting of Catastrophism * Lyell's Defense of Time's Cycle * Lyell, Historian of Time's Cycle * The Partial Unraveling of Lyell's World View * Epilogue *5. Boundaries * Hampton's Throne and Burnet's Frontispiece * The Deeper Themes of Arrows and Cycles * Bibliography * Index

Time's Arrow, Time's Cycle: Myth and Metaphor in the Discovery of Geological Time

A general two-site solution for the chemical exchange produced dependence of T2 upon the carr-Purcell pulse separation

Progress in any field depends primarily on our ability to synthesize previous experience – to stand on the shoulders of the giants who have worked before us. In fisheries management we have learned a great deal from past experience, but we have also failed to do so. Most stock assessments use no quantitative information derived from previous experience on other fish stocks, and often fix parameter values at some ‘best’ estimates rather than admit uncertainty in their value. Meta-analysis provides a method to admit the uncertainty in most model parameters while using experience from other populations to provide an estimate of the distribution of the parameter. We demonstrate the application of meta-analysis for the intensity of depensation in spawner–recruit relationships in two species of Pacific salmon, and we discuss the potential of, and limitations to, meta-analysis in fisheries stock assessment.

Standing on the Shoulders of Giants: Learning from Experience in Fisheries

Classical magnetic dipolar interactions can make significant contributions to magnetic anisotropy in amorphous ferrimagnetic alloys with slight structural anisotropies on either atomic or microstructural scales. Simple expressions have been derived for this magnetic anisotropy in terms of structural anisotropy parameters, p, V, and Δx. For an alloy with atomic‐scale structural anisotropy (pair ordering), p is a measure of alignment of unlike nearest‐neighbor pairs. For an alloy with aligned elongated composition inhomogeneities, V is the volume fraction of inhomogeneities and Δx is the composition difference (atom fraction) between the inhomogeneities and their surroundings. Accounting for magnetic anisotropy observed experimentally in bias‐sputtered GdCo‐based alloy films solely in terms of pair ordering and classical dipolar interactions requires p∼0.015. Accounting for the anisotropy solely in terms of composition inhomogeneities requires Δx∼0.1 for V=0.5. Although such atomic‐scale structural anisotro...

Magnetic anisotropy from dipolar interactions in amorphous ferrimagnetic alloys

The semiclassical resonance theory for a system of coupled magnetic sublattices is briefly reviewed and some similarities and differences of ferromagnetic and ferrimagnetic resonance considered. The use of the effective gyromagnetic ratio simplifies the interpretation of many experimental results for g-values. The qualitative application of this concept to some related phenomena shows that they can have features characteristic of the ferrimagnetic case.

Roald K. Wangsness

Papers

Ferrimagnetic Resonance and Some Related Effects

On the Shoulders of Giants (Cont.)

Note on the Separation of Relativistically Moving Rockets

Lectures on Matter and Equilibrium

Masers and Lasers