phy246s11_hw2sol

phy246s11_hw2sol - normalized eigenfunctions 6(xt rlv and...

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Physlss 216 Second Homework Set Due: Februarv 4.2011 1. Consider a wa,ve function of Lorentzian form, i.e., ,[email protected]) a ) \Vhat are b) \Vha,t are c) Compare vvith the uncertainty relation. 2. Consider the SHO Hamiltonian |[= I o 1 o 2 = 1;P- * ,mw- x a) Show that e-o1' and re-or2 are eigenfunctions of I/ for appropriate choice of a. \\Ihat are the eigenvalues? b) Take $(x,t =- 0) = (A+ Bx)e-os2 . Find < r >1 and <J.)r. Explain why these must vanish if either A or B is zero. 3. Consider a particle of mass M in-lf dimensions u,ith ,r:f #*[email protected]) i=I --'- u,here lt(x) - 0 for all cl for which 0 ( cl ( I and V(xr)= oo otherr,,,ise. a) \Vhat are the
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Unformatted text preview: normalized eigenfunctions 6(xt,. .. rlv) and their eigenvalues? b) \Vhat are the ten lowest eigenvalues? (Assume N > b.) c) How many distinct states are there for ea,ch of ihese ten energies? x f,t4€*r* +F *,cg-=, {l--l r '-l !' ,f ; t*! + ^\- r! ^,-'d A]' 'f \ i1 I ^**"-i--._.'(h}=!a*;**L#+d#*J6*''.ilLn-;-t'"}.t]***' = (L ;*.'":Lf+ u.^ li*ll- ;'u:li ^ s+9^re'*l : ( = -"-f +ei. .i=o f^n" g,;t* ^*^i tf6at"1iatrsl4i*t j' ^-:._ rt I A*-Ldb*s)+ - *h (*ux.'.6)r;;t*'+$) ]i Fi-:-:,L1i,iAsi I-;i6ur'+Gi=.*f ,rl-*-[\] f5,; -- -r L-Lr* - l,f*J-r"'-a L-j lr* #* i€ *L t-* 2-dr)* e t-ftJ dttl i) ra J"-** 't-;t...
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phy246s11_hw2sol - normalized eigenfunctions 6(xt rlv and...

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