Summary of "Quantum mechanics as a framework. Defining linearity"

Quantum mechanics is a framework that has replaced classical physics as the correct description of fundamental theory.

Quantum mechanics applies to various physical phenomena such as electromagnetism, strong interaction, photons, and gravitation.

Quantum mechanics began with the work of Planck and Einstein in the late 19th and early 20th centuries.

Quantum mechanics is a framework applied to many things, including quantum electrodynamics, quantum chromodynamics, quantum optics, and quantum gravity.

The video aims to cover five topics: linearity, complex numbers, loss of determinism, superposition, and entanglement.

linearity in Quantum mechanics

linearity in Quantum mechanics is a fundamental aspect where solutions can be added or scaled by a constant number.
linearity is exemplified in Maxwell's theory of electromagnetism, where solutions can be combined without affecting each other.
A linear equation is defined as L(u) = 0, where L is a linear operator acting on the unknown variable u.
The linear operator must satisfy properties such as L(a*u) = a*L(u) and L(u1 + u2) = L(u1) + L(u2) to be considered linear.
An example of a linear equation is provided with a differential equation D(u)/D(t) + 1/tau*u = 0, where L(u) is defined as B*(d/dt)(u) + 1/tau*u.