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Unformatted text preview: Lecture I: Dirac Notation To describe a physical system, QM assigns a complex number (`amplitude) to each distinct available physical state. (Or alternately: two real numbers) What is a `distinct physical state? Consider a system with M distinct available states The 2M real numbers can be viewed as a vector in an 2Mdimensional realvalued vector space Or alternatively as a vector in an Mdimensional complexvalued vector space We will refer to this abstract vector space as `Hilbert Space or `state space Any vector in this space corresponds to a possible quantummechanical state. The number of such quantum states is uncountable infinity Just as calculus provides the mathematical basis for Classical Mechanics, the mathematical basis for QM is linear algebra Vectors, matrices, eigenvalues, rotations, etc are key concepts Various common vector notations: 1. Vector notation: Just a name, an abstraction that refers to something physical 2. Unit vectors: Unit vectors are predefined in physical terms...
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This note was uploaded on 12/02/2010 for the course PHYSICS 851 taught by Professor M.moore during the Fall '09 term at Michigan State University.
 Fall '09
 M.Moore
 mechanics

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