A Mathematical Journey to Quantum Mechanics

G. Aravind, Ayush Goyal, Narasimhaiengar Mukunda +1 more

Giuseppe Dito

This text explores the profound and beautiful interplay between quantum physics and mathematics. We journey from the crisis of classical physics at the turn of the 20th century to the elegant, abstract mathematical frameworks that define modern quantum mechanics. We will see how physical problems forced the invention of new mathematics and how mathematical structures, in turn, provided the language to describe the quantum realm. Key figures like Planck, Einstein, Heisenberg, Born, von Neumann, Weyl, and Dirac will guide us,revealing a story where physical intuition and mathematical formalism are inextricably linked.

A. Mangoni

Anirban Pathak

It is not in the scope of this elementary textbook to introduce quantum mechanics in detail or to provide an elaborate mathematical background required for quantum computing. However, we will provide some basic ideas that are essential for us to proceed further. To be precise, here we will briefly describe vector space, different types of operators, Gram-Schmidt procedure, postulates of quantum mechanics, POVM, density operator, entanglement and its measures, partial trace, Schmidt decomposition, Bloch sphere, nocloning theorem, etc. Let us start our journey toward the world of quantum computation by reviewing some simple ideas of algebra.

David A. Edwards

Brian C. Hall