Lect5_Postulates - Remark: Commutation of Operators Since...

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Unformatted text preview: Remark: Commutation of Operators Since operators are matrices, they do not necessarily commute We define the commutator of the operators A and B as The properties of most physically important operators (e.g. X, P, L, S, ) can generally be deduced solely from their commutation relations BA AB ! [ ] BA AB B A ! = , Lecture 5: Postulates of QM MOTIVATION TO STUDY QM: Quantum mechanics underlies Nuclear, Particle, Condensed Matter, and Atomic physics (and is thus very important for Astronomy and Astrophysics) Quantum mechanics explains the periodic table and Chemistry When tested, Quantum Mechanics has always been found to be correct Some predictions of QM tested to ten decimal places of precision Quantum Mechanics is self-consistent, there are no paradoxes So called paradoxes of QM are merely points where its predictions conflict with classical intuition about the nature of reality The meaning of Quantum Mechanics is not understood The key difficulty is the origin of the randomness inherent in QM Is true randomness logically tenable? Very different interpretations are equally valid Many-worlds, Bohmian mechanics, Question #1 Suppose a particle has the wavefunction: If the position of the particle is measured, what will the result of the measurement be? 2 2 2 ) ( 4 2 1 ) ( ! "! # x x e x $ $ = Statement of the Postulates 1. At a fixed time t , the state of a physical system is defined by specifying a ket | ! ( t ) " belonging to the state space of the system 2. Every measureable physical quantity is described by a Hermitian operator A acting in the state space...
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Lect5_Postulates - Remark: Commutation of Operators Since...

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