PHY3063 R. D. Field Department of Physics Chapter6_8.doc University of Florida The Infinite Square Well (2) Normalized Wavefunctions: Now we require that 1)()(=∫∞∞−∗dxxxnnψ, and hence 12sin4)/(sin42022022===∫∫LAdnLAdxLxnAnLπθ. Thus ,LA2/1=and h/)(),(tiEnnnextx−=Ψwith )/sin(2)(LxnLxn=. Probability Density:The probability density for the nthstate is )/(sin2|),(|)(22LxnLtxxnnρ=Ψ=.Note that ρnand not a function of time! These states are “stationary states”(i.e.independent of time). Average Value of x:The average position for the nthstate is 242)(sin2)/(sin2)()(2222022202*LnnLdnLdxLxnxLdxxxxxnLn====ΨΨ=><∫∫∫∞∞−Average Value of x2:The average value of x2in the nthstate is −=
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Sin, Fundamental physics concepts, Department of Physics, R. D. Field, nth state