PHY3063 R. D. Field Department of Physics Chapter7_12.doc University of Florida Two Particles in a Box One Particle in a One-Dimensional Box: For one particle in a box (V(x) = ∞x ≤0,V(x) = ∞x ≥Land V(x) = 00 < x < L) we found h/)(),(tiEnnnextx−=Ψψwith )/sin(2)(LxnLxnπ=. The energy levels are given by 0222222EnmLnEn==hwhere 22202mLEh=. Two Particles in a One-Dimensional Box: For two (non-interacting) particles we look for a solution of the form hh/21/2121)()(),(),,(iEtiEtexxexxtxx−−==Ψwith Empmpxx=+2)(2)(2221. Thus, ),(),(2),(221222122212122xxEdxxxdmdxxxdm=−−hh)()()()(2)()(221222212211222xxEdxxdxmdxxdxm=−−hhEdxxdxmdxxdxm=−−222222211212)()(12)()(12hhHence, E = E1+ E2and )()(21121122xEdxxdm=−h)()(22222222xEdxxdm=−hThe total energy is therefore given by 22222212)()()(mLEEEβααβ+=+=h222212)(mLEh=22222
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This note was uploaded on 05/29/2011 for the course PHY 3063 taught by Professor Field during the Spring '07 term at University of Florida.