Lect2_DiracNot - Lecture I Dirac Notation To describe a...

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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 2M-dimensional real-valued vector space Or alternatively as a vector in an M-dimensional complex-valued 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 quantum-mechanical 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
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Various common vector notations: 1. Vector notation: Just a name, an abstraction that refers to something physical 2. Unit vectors:
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