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Lect1_DiracNot

# Lect1_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 possible physical state. i.e. 2 real numbers per state In Classical mechanics, a system must have a single state, while in QM arbitrary superpositions are allowed Consider a system with M distinct possible states The 2xM real numbers can be viewed as a vector in an 2xM-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 Just as calculus is necessary to do 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:

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Lect1_DiracNot - Lecture I Dirac Notation To describe a...

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