05_03_04 - Georg.Hoffstaetter@Cornell/04/2005 Two quantum particles Finding the probability to have particle 1 in the interval[x 1,x 1 dx 1 and

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Unformatted text preview: Georg.Hoffstaetter@Cornell.edu 72 03/04/2005 Two quantum particles Finding the probability to have particle 1 in the interval [x 1 ,x 1 +dx 1 ] and finding particle 2 in [x 2 ,x 2 +dx 2 ] for example in a diatomic molecule. 2 1 2 2 1 | ) , ( | dx dx x x Φ ) , ( ) , ( ) ( ) , ( ) , ( 2 1 2 1 2 1 2 1 2 2 1 2 2 2 2 2 2 2 1 2 1 2 x x E x x x x V x x x x x m x m Φ = Φ- + Φ- Φ- ∂ ∂ ∂ ∂ ) , ( ) ( ) , ( ) ( ) , ( ) , ( ) ( ) , ( ) ( ) , ( 2 1 2 2 1 2 1 2 1 2 2 1 1 2 1 2 1 2 1 2 2 2 2 2 2 2 1 2 1 2 x x E E x x x x V x x x x E E x x x x V x x kin pot x m kin pot x m Φ + = Φ- + Φ- Φ + = Φ- + Φ- ∂ ∂ ∂ ∂ ✁ ✁ For a fixed total energy E one obtains for fixed x 2 fixed x 1 Schrödinger equation for two particles ● is now replaced by and is replaced by in the energy equation 1 p 1 x i ∂ ∂- ! 2 p 2 x i ∂ ∂- ! E V m p m p = + + 2 2 2 1 2 1 2 2 2 1 kin kin pot E E E E + + = Georg.Hoffstaetter@Cornell.edu 73 A diatomic molecule therefore has a de Broglie wavelength that corresponds...
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This note was uploaded on 09/28/2008 for the course PHYS 316 taught by Professor Hoffstaetter during the Spring '05 term at Cornell University (Engineering School).

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05_03_04 - Georg.Hoffstaetter@Cornell/04/2005 Two quantum particles Finding the probability to have particle 1 in the interval[x 1,x 1 dx 1 and

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