Conceptual and mathematical aspects of quantum mechanics

Dennis Morris

This introduction to quantum mechanics is both reader-friendly and complete. Tit covers the conceptual and philosophical aspects of quantum mechanics before gently presenting the mathematics underlying the subject. After a chapter on the history of the theory, the whole of quantum mechanics is then presented, followed by applications of the theory and a revision chapter.

Stephen J. Gustafson, Israel Michael Sigal

Stephen J. Gustafson, Israel Michael Sigal

Miguel Gallego, Borivoje Dakić

The quantum description of the microscopic world is incompatible with the classical description of the macroscopic world, both mathematically and conceptually. Nevertheless, it is generally accepted that classical mechanics emerges from quantum mechanics in the macroscopic limit. In this paper, we challenge this perspective and demonstrate that the behaviour of a macroscopic system can retain all aspects of the quantum formalism, in a way that is robust against decoherence, particle losses and coarse-grained (imprecise) measurements. This departure from the expected classical description of macroscopic systems is not merely mathematical but also conceptual, as we show by the explicit violation of a Bell inequality and a Leggett–Garg inequality.

Stephen J. Gustafson, Israel Michael Sigal

Marco Giliberti, Luisa Lovisetti

Abstract In a cultural, history-based, sense-making approach to Quantum Mechanics multi-representations are fundamental to improve conceptual learning of abstract, mathematical aspects. In fact, they can be integrated among each other allowing students to actively manipulate concepts and instruments which would otherwise be difficult and little accessible. In this presentation we will show different (and interconnected) representations of vectors in complex Hilbert spaces and of eigenvalues and eigenvectors of Hermitian matrices together with an evaluation of their efficacy for students conceptual understanding.