# Lectures on Quantum Mechanics for mathematicians

## TL;DR

This paper introduces quantum mechanics concepts to mathematicians, discusses the mathematical interpretation of quantum phenomena, and proposes a dynamical interpretation based on nonlinear PDE attractors, supported by various model results.

## Contribution

It offers a new dynamical interpretation of quantum phenomena using attractors of nonlinear Hamiltonian PDEs, with partial confirmations and open problems.

## Key findings

- Confirmed attractor conjectures for several nonlinear PDE models since 1990
- Calculated diffraction amplitude for electron scattering using Kirchhoff approximation
- Identified open problem for Maxwell–Schrödinger equations

## Abstract

The main goal of these lectures -- introduction to Quantum Mechanics for mathematically-minded readers. The second goal is to discuss the mathematical interpretation of the main quantum postulates: transitions between quantum stationary orbits, wave-particle duality and probabilistic interpretation. We suggest a dynamical interpretation of these phenomena based on the new conjectures on attractors of nonlinear Hamiltonian partial differential equations. This conjecture is confirmed for a list of {\it model Hamiltonian nonlinear} PDEs by the results obtained since 1990 (we survey sketchy these results). However, for the Maxwell--Schr\"odinger equations this conjecture is still an {\it open problem}. We calculate the diffraction amplitude for the scattering of electron beams and Aharonov--Bohm shift via the Kirchhoff approximation.