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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 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 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...
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This note was uploaded on 12/21/2011 for the course PHY 851 taught by Professor Moore,m during the Fall '08 term at Michigan State University.
- Fall '08