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Unformatted text preview: 58 CHAPTER 5. MULTIPLE-PARTICLE 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 vice-versa. 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. Real-life 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