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Unformatted text preview: 58 CHAPTER 5. MULTIPLEPARTICLE SYSTEMS approximation. For example, two electrons repel each other. All else being the same, the electrons would rather be at positions where the other electron is nowhere close. As a result, it really makes a difference for electron 1 where electron 2 is likely to be and viceversa. To handle such situations, usually sums of product wave functions are used. However, for some cases, like for the helium atom, a single product wave function is a perfectly acceptable first approximation. Reallife electrons are crowded together around attracting nuclei and learn to live with each other. Answer: The probability of finding particle 1 within a vicinity d 3 vectorr 1 of vectorr a and particle 2 within a vicinity d 3 vectorr 2 of vectorr 2 is: ψ 1 ( vectorr a ) ∗ ψ 2 ( vectorr 2 ) ∗ ψ 1 ( vectorr a ) ψ 2 ( vectorr 2 ) d 3 vectorr 1 d 3 vectorr 2 while the corresponding probability of finding particle 1 within a vicinity d 3 vectorr 1 of vectorr b and particle 2 within a vicinity d 3 vectorr 2 of vectorr 2 is: ψ 1 ( vectorr b ) ∗ ψ 2 ( vectorr 2 ) ∗ ψ 1 ( vectorr b ) ψ 2 ( vectorr 2 ) d 3 vectorr 1 d 3 vectorr 2 . Taking the ratio of the two probabilities, the chances of finding particle 1 at vectorr a versus finding it at vectorr b are the same wherever particle 2 is likely to be found.are the same wherever particle 2 is likely to be found....
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This note was uploaded on 11/13/2011 for the course PHY 4458 taught by Professor Garvin during the Fall '11 term at University of Florida.
 Fall '11
 GARVIN

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