Review of Classical Mechanics

G.C. Stey

Johan Falk

This thesis presents a comprehensive review of research into students’ depictions of quantum mechanics. A taxonomy to describe and compare quantum mechanics education research is presented, and this taxonomy is used to highlight the foci of prior research. A brief history of quantum mechanics education research is also presented. Research implications of the review are discussed, and several areas for future research are proposed. In particular, this thesis highlights the need for investigations into what interpretations of quantum mechanics are employed in teaching, and that classical physics – in particular the classical particle model – appears to be a common theme in students’ inappropriate depictions of quantum mechanics. Two future research projects are presented in detail: one concerning interpretations of quantum mechanics, the other concerning students’ depictions of the quantum mechanical wave function.This thesis also discusses teaching implications of the review. This is done both through a discussion on how Paper 1 can be used as a resource for lecturers and through a number of teaching suggestions based on a merging of the contents of the review and personal teaching experience.

Juan José García‐Ripoll

In this chapter, we review basic concepts from quantum mechanics that will be required for the study of superconducting quantum circuits. We review the fundamental idea of energy quantization and how this can be formalized, using Dirac's ideas, to develop a quantum mechanical description that is consistent with the classical theory for a comparable object. We review the notions of quantum state, observable and projective and generalized measurements, particularizing some of these ideas to the simple case of a two-dimensional object or qubit.

EDWARD B. NELSON

Stochastic mechanics is an interpretation of nonrelativistic quantum mechanics in which the trajectories of the configuration, described as a Markov stochastic process, are regarded as physically real. The natural stochastic generalization of classical variational principles leads to a derivation of the Schrödinger equation. A brief review of the successes and failures of the theory is given, with references.