The Errors of Feynman and Hibbs

In 1965, Richard Feynman and his former graduate student Albert Hibbs published a textbook on Quantum Mechanics and Path Integrals. This text — based on Feynman’s teaching of graduate-level quantum mechanics courses at CalTech — is full of remarkable insight and excruciating errors. The errors have been corrected through an emended edition. This article investigates the source of those errors

The Geometrical Significance of the Laplacian

The Laplacian operator can be defined, not only as a differential operator, but also through its averaging properties. Such a definition lends geometric significance to the operator: a large Laplacian at a point reflects a “nonconformist” (i.e., different from average) character for the function there. This point of view is used to motivate the wave equation for a drumhead

Insight into entropy

What is the qualitative character of entropy? Several examples from statistical mechanics (including liquid crystal reentrant phases, two different lattice gas models, and the game of poker) demonstrate facets of this difficult question and point toward an answer. The common answer of entropy as disorder is regarded here as inadequate. An alternative but equally problematic analogy is entropy as freedom.\u27\u27 Neither simile is perfect, but if both are used cautiously and not too literally, when the combination provides considerable insight

My Favorite Exam Question

My favorite exam question comes from the final exam in an introductory mechanics course: A rolling 31 ton railroad boxcar collides with a stationary flatcar. The coupling mechanism activates so the cars latch together and roll down the track attached. Of the initial kinetic energy, 38% dissipates as heat, sound, vibrations, mechanical deformation, and so forth. How much does the flatcar weigh