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Unformatted text preview: on the amplitude and , (7.30) Now the probability to find the particle at position , where is proportional to the time spent in an area around . The time spent in its turn is inversely proportional to the velocity (7.31) Solving in terms of we find (7.32) Doing the integration of over from to we find that the normalised probability is (7.33) We now would like to compare this to the quantum solution. In order to do that we should consider the probabilities at the same energy, (7.34) which tells us what to use for each , (7.35) So let us look at an example for . Suppose we choose and such that . We then get the results shown in Fig. 7.2 , where we see the correspondence between the two functions....
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- Fall '10
- Physics, interesting questions, classical probabilities, uantum-Classical Correspondence, normalised probability