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Unformatted text preview: 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 twoslit 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 dont have a conceptual models or examples to help form a intuition about what is happening. Thats 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. 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 . 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 thesebut 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. 4/7/2004 H133 Spring 2004 3 Rule #1 The State Vector Rule The state of a quanton at a given time is described by using a normalized state vector y> having a certain number of complex components. In the context of a certain subset of observables, a quantons state vector has as many components as there are possible values for any one of the subsets basic observables. Even so, the components of this vector do not correspond to the values of that or any other observable. There is a lot going on here lets break it down (A) Components: Complexjust a statement we use complex numbers....
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 Spring '11
 Furnstahl
 mechanics, Quantum Physics

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