L15_QM - Lecture 15: Introduction to Quantum Mechanics...

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PHYS126, L15: page 1 of 4 Lecture 15: Introduction to Quantum Mechanics Shengwang Du, 28&30 March 2011 [Powerpoint slides: introduction] 1. Classical (Relativity) versus quantum way of thinking Newtonian Mechanics: Motion equation: 2 2 dt r d m a m F r r r = = Initial condition: } , , { ) 0 ( 0 0 0 0 z y x r t r = = = r r , 0 ) 0 ( v t v r r = = Relativistic Mechanics: Motion equation: = = dt r d m dt d dt P d F r r r γ Initial condition: } , , { ) 0 ( 0 0 0 0 z y x r t r = = = r r , 0 ) 0 ( v t v r r = = [Powerpoint slide] In both Newtonian and Relativistic Mechanics, motion of an object is described by the motion equation (governed by force) and initial values of position and velocity. In other word, with the motion equation, you can precisely predict the future of an object if you know its initial values of position and velocity. The state of a particle is described by its displacement ) ( t r r and velocity ) ( t v r (or momentum): State : ) ( t r r & ) ( t v m P r r = mg r 0 ,v 0 r (t), v (t)
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PHYS126, L15: page 2 of 4 Therefore, the Newtonian and relativistic mechanics depend on that the position and momentum of an object can be determined simultaneously. Question: What will happen if you are told by the creator that the position and momentum can not be determined at the same time? Quantum Mechanics Heisenberg uncertainty relations 2 / h Δ Δ p x [Beiser Ch 3 Eq. (3.21)] In Quantum Mechanics, talking about ) ( t r r and ) ( t v r at the same time is meaningless. In other word, Quantum Mechanics is not interested in talking bout an individual event about ) ( t r r and ) ( t v r that is the main task of classical (relativistic) mechanics. Quantum Mechanics does not intend to tell you the details of orbit ) ( t r r and velocity ) ( t v r of an individual event in the time and space -----this is the most difficult thing for people to understand because we always think about an object at some position with some velocity. In Quantum Mechanics, the state of a given system (or a particle) is completely described
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L15_QM - Lecture 15: Introduction to Quantum Mechanics...

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