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Lecture# Introduction to Quantum Mechanics

Description

This lecture covers the introduction to quantum mechanics, focusing on S-matrix, Møller operators, and scattering amplitudes. The instructor explains the evolution in the Dirac picture, isometric and unitary conditions, and the optical theorem.

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In course

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Related concepts (40)

Related lectures (60)

PHYS-425: Quantum physics III

To introduce several advanced topics in quantum physics, including
semiclassical approximation, path integral, scattering theory, and
relativistic quantum mechanics

Reading

Reading is the process of taking in the sense or meaning of letters, symbols, etc., especially by sight or touch. For educators and researchers, reading is a multifaceted process involving such areas as word recognition, orthography (spelling), alphabetics, phonics, phonemic awareness, vocabulary, comprehension, fluency, and motivation. Other types of reading and writing, such as pictograms (e.g., a hazard symbol and an emoji), are not based on speech-based writing systems.

Reading comprehension

Reading comprehension is the ability to process written text, understand its meaning, and to integrate with what the reader already knows. Reading comprehension relies on two abilities that are connected to each other: word reading and language comprehension. Comprehension specifically is a "creative, multifaceted process" dependent upon four language skills: phonology, syntax, semantics, and pragmatics.

Gifford Lectures

The Gifford Lectures (ˈgɪfərd) are an annual series of lectures which were established in 1887 by the will of Adam Gifford, Lord Gifford. Their purpose is to "promote and diffuse the study of natural theology in the widest sense of the term – in other words, the knowledge of God." A Gifford lectures appointment is one of the most prestigious honours in Scottish academia. The lectures are given at four Scottish universities: University of St Andrews, University of Glasgow, University of Aberdeen and University of Edinburgh.

Reading frame

In molecular biology, a reading frame is a way of dividing the sequence of nucleotides in a nucleic acid (DNA or RNA) molecule into a set of consecutive, non-overlapping triplets. Where these triplets equate to amino acids or stop signals during translation, they are called codons. A single strand of a nucleic acid molecule has a phosphoryl end, called the 5′-end, and a hydroxyl or 3′-end. These define the 5′→3′ direction. There are three reading frames that can be read in this 5′→3′ direction, each beginning from a different nucleotide in a triplet.

Invertible matrix

In linear algebra, an n-by-n square matrix A is called invertible (also nonsingular, nondegenerate or (rarely used) regular), if there exists an n-by-n square matrix B such that where In denotes the n-by-n identity matrix and the multiplication used is ordinary matrix multiplication. If this is the case, then the matrix B is uniquely determined by A, and is called the (multiplicative) inverse of A, denoted by A−1. Matrix inversion is the process of finding the matrix B that satisfies the prior equation for a given invertible matrix A.

Explores scattering theory, S-matrix, T-product, perturbation theory, and Schrödinger equation solutions.

Covers the derivation of the scattering amplitude using Lippmann-Schwinger equations and the introduction of Green's functions.

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Explores scaling and renormalization in statistical mechanics, emphasizing critical points and invariant properties.

Discusses the scattering problem, differential cross-section, total cross-section, and Moller operators in quantum mechanics.