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?’
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{: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 hem5; 20L(1r/Ck) 
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_ 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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 Spring '10
 Chang
 Physics

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