The mathematical formulations of quantum mechanics are those mathematical formalisms that permit a rigorous description of quantum mechanics. This mathematical formalism uses mainly a part of functional analysis, especially Hilbert spaces, which are a kind of linear space.

Quantum mechanics can be baffling, yes, surprising, definitely, and certainly counter-intuitive. That’s because quantum mechanics lives outside of our everyday lives and any attempt to explain quantum phenomena using classical physics fails. Quantum mechanics just is, and it’s awesome!

Quantum mechanics allows the calculation of properties and behaviour of physical systems. It is typically applied to microscopic systems: molecules, atoms and sub-atomic particles.

A fundamental physical constant occurring in quantum mechanics is the Planck constant, h. A common abbreviation is ħ = h/2π, also known as the reduced Planck constant or Dirac constant. The general form of wavefunction for a system of particles, each …

The whole of quantum mechanics can be expressed in terms of a small set of postulates. When their consequences are developed, they embrace the behaviour of all known forms of matter, including the molecules, atoms, and electrons that will be at the centre of our attention in this book. This chapter

In the analysis of fundamental questions, it will be shown how the statistical formulas of quantum mechanics can be derived from a few qualitative, basic assumptions.

Oct 18, 2022 · This book provides the rigorous mathematical foundations of Quantum Physics, from the operational meaning of the measuring process to the most recent theories for the quantum scale of space-time geometry.

Lecture 1: An overview of quantum mechanics. Quantum mechanics as a framework. Defining linearity (17:46) Linearity and nonlinear theories. Schrödinger’s equation (10:01) The nature of superposition. Mach-Zehnder interferometer (14:30) Lecture 2: Overview of quantum mechanics (cont.). Interaction-free measurements. More on superposition.

A very readable introduction to modern mathematical topics in quantum mechanics; Solves the problem of how to teach quantum mechanics to mathematically oriented students in an optimal way; Shows how the mathematical treatment of quantum mechanics brings insights to physics; Useful guide to the literature

These notes are a quick and-dirty outline of the simplest mathematical setting of quantum mechan ics. None of it should be taken too seriously: real physics is hard, and requires more than a few nice mathematical ideas. In order to describe a toy picture of quantum mechanics, I’ll start with a toy picture of classical mechanics.