4_pdfsam_Quiz 7-10 solutions

4_pdfsam_Quiz 7-10 solutions - A particle of mass m moves...

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Unformatted text preview: A particle of mass m moves in a 1—dimensional infinite square well of width 2a. The well is centered about X = 0, located in the interval between —a and a. The potential U = 0 for this region where —a < X < a, and is infinite elsewhere. a. Write down the wave function for the ground state and the 15‘ excited state, and their respective energies (1 + 1 + l + 1 points; 4 points total). Provide the normalization for the ground state only. Gmm’k S‘lwlre'. tl)‘,(.>< E) 2J1. COS(1%§:U :(gden : 39m0t?’ 1e wags state ”t Cr 0*: \E emf-”£53 {:1 2 L1 : LlEt Elmo} b. For the ground state, compute <x2>, the ixpectation value of x2 (2 points). we '2. 'L <f>= 333% x Ll(I on : 53; CO;- 7334* "on _ 0x a X1” K1 m *1 Xi’la + Ll“— 8(le = eta—3+ at we»): at ,a m i t '3. 'L ‘ . . ‘1 Will/L ix‘ccgm lo‘d Port—g] lWICL' EX?- £03 (C )0 0W0; : RX (2050?) 4' (ex CZSMCK) + (n hem-5; 20L(1r/Ck) - , $3-199: .. '2— ‘ :8. N .L _ 3 1‘1 ("3: 'It A, o.l’$a I ' c. The infinite potential outside the square well region is now reduced to a finite value U = Uo > 0. Write down the function form of the ground state wave function for the regions outside the well, where X < -a , and x > a.(1 PM)? (,0th C= m 47} gm X)“ J Kl} N eacx l Kl/INe’J. for X<m ...
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