PHY4604 R. D. Field Department of Physics Chapter5_4.doc University of Florida Two Fermion Ground State Probability Density00.51x2/Lx1= 0.5 LFermi-DiracBosons and Fermions in a Box Two Particles in a Box: For the problem of two particles in a one dimensional box (0 ↔L) we have )2/()(22222mLEβαπαβ+=hand())/(sin)/(sin)/(sin)/(sin2),(22122212221LxLxLxLxLxxclassicalαπβπρ+=)/sin()/sin()/sin()/sin(4),(2211221intLxLxLxLxLxx=Note that 1),(2121=∫∫LLclassicaldxdxxxand δ=dxdxxx2121int),(. Ground State for Two Fermions: The lowest energy state for two fermions is α= 1 and β= 2(or α= 2 and β= 1) and FDEmLE022212)2/(5==hand )/(sin)/2(sin)/2(sin)/(sin2),(2212221222112LxLxLxLxLxxclassical+=)/2sin()/sin()/2sin()/sin(4),(2211221int12LxLxLxLxLxx=),(),(),(21int1221122112xxxxxxclassicalFD−=. Put one particle at x1= 0.5Land plot the probability of finding the other particle at x2:)/2(sin2),5.0(2222112LxLxLxFD==. Ground State for Two Bosons:
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This note was uploaded on 05/29/2011 for the course PHY 4064 taught by Professor Fields during the Spring '07 term at University of Florida.