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LectureQ6

# LectureQ6 - Chapter 6 Special Note Professor Heinz may...

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4/7/2004 H133 Spring 2004 1 Chapter 6 We have explored the some of the evidence that led to the formulation of quantum mechanics. Now we need to start to develop the mathematic model for quantum mechanics which will allow us to explain the experiments we have discussed. We are going to take the following approach Develop a set of rules for quantum mechanics. We will accept these rules as correct Define something called a “Wavefunction”. This is the key function (discrete and continuous) that define the state of our system. We will see how the rules and the wavefunction allow us to predict our observations with SG devices and with the two-slit experiment with particles. Note: Quantum Mechanics is not like the other theories that we have studied in the past. In quantum mechanics the mathematical model makes a direct connection to the observation. We don’t have a conceptual models or examples to help form a intuition about what is happening. That’s just something we will have to live with in the strange world of quantum mechanics. Special Note: Professor Heinz may start lecturing on this chapter. He may not necessarily follow these notes. I will finish this chapter.

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4/7/2004 H133 Spring 2004 2 “Observables” All quanta have a set of intrinsic characteristics that help define what that object is Mass, Electric charge, Spin, etc. These never change for a particle and it is these quantities that define the particle. An electron is an object with mass 0.511 MeV/c 2 , -1 electric charge, and spin of ½ . All quanta also have a set of quantities which we call “observables”, which we can measure experimentally. Position, Momentum, Energy, Spin Projection We will deal mostly with these…but there are others too. When we perform and experiment these are the quantities we normally determine and by measuring these we can often extract the intrinsic characteristics. We will divide “observables” into two different groups Spin Subset (S x , S y , S z ) Position Subset (x, p) Included in these subsets are other variables that can be determined from the basic components of the subset. e.g. E = p x 2 /2m + V(x) can be determined from x, p. Normally, these two subsets are independent of one another and therefore we can consider one at a time.