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Lecture# Quantum Mechanics I

Description

This lecture covers the analysis of composite systems in quantum mechanics, focusing on systems with two or more components. Topics include tensor product spaces, linear combinations, operators acting on composite spaces, the concept of measurements, entanglement, Bell's inequalities, and the implications of quantum entanglement on non-locality and communication. The lecture also discusses the concept of separability, the Einstein-Podolsky-Rosen paradox, and the experimental verification of quantum entanglement. The instructor explains the Bell inequalities and the limitations of hidden variable theories through a thought experiment involving black and white boxes. The lecture concludes with a brief overview of Bell's theorem and its experimental confirmation.

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Instructors (2)

Related concepts (32)

PHYS-313: Quantum physics I

The objective of this course is to familiarize the student with the concepts, methods and consequences of quantum physics.

Quantum entanglement is the phenomenon that occurs when a group of particles are generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the group cannot be described independently of the state of the others, including when the particles are separated by a large distance. The topic of quantum entanglement is at the heart of the disparity between classical and quantum physics: entanglement is a primary feature of quantum mechanics not present in classical mechanics.

In physics, the principle of locality states that an object is influenced directly only by its immediate surroundings. A theory that includes the principle of locality is said to be a "local theory". This is an alternative to the concept of instantaneous, or "non-local" action at a distance. Locality evolved out of the field theories of classical physics. The idea is that for a cause at one point to have an effect at another point, something in the space between those points must mediate the action.

Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with local hidden-variable theories, given some basic assumptions about the nature of measurement. "Local" here refers to the principle of locality, the idea that a particle can only be influenced by its immediate surroundings, and that interactions mediated by physical fields cannot propagate faster than the speed of light.

A Bell test, also known as Bell inequality test or Bell experiment, is a real-world physics experiment designed to test the theory of quantum mechanics in relation to Albert Einstein's concept of local realism. Named for John Stewart Bell, the experiments test whether or not the real world satisfies local realism, which requires the presence of some additional local variables (called "hidden" because they are not a feature of quantum theory) to explain the behavior of particles like photons and electrons.

In physics, hidden-variable theories are proposals to provide explanations of quantum mechanical phenomena through the introduction of (possibly unobservable) hypothetical entities. The existence of fundamental indeterminacy for some measurements is assumed as part of the mathematical formulation of quantum mechanics; moreover, bounds for indeterminacy can be expressed in a quantitative form by the Heisenberg uncertainty principle.

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