A particle moves in an infinite potential well described by x>a/2, V(x) = { 00, ||...

  

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A particle moves in an infinite potential well described by x>a/2, V(x) = { 00, || ≤a/2. The eigenfunctions are of the form n(x) = An cos (knt), or un(x) = Bn sin (knx), depending on the value of n. For n = 3, 3(x) =(√2/a) cos (3mx/a) for r ≤ a/2 and 23 (2) = 0 for |*|> a/2. (a) What are the expectation values of r and r² in the n = 3 state. (b) What are the expectation values of p and p² in the n = 3 state. A particle moves in an infinite potential well described by x>a/2, V(x) = { 00, || ≤a/2. The eigenfunctions are of the form n(x) = An cos (knt), or un(x) = Bn sin (knx), depending on the value of n. For n = 3, 3(x) =(√2/a) cos (3mx/a) for r ≤ a/2 and 23 (2) = 0 for |*|> a/2. (a) What are the expectation values of r and r² in the n = 3 state. (b) What are the expectation values of p and p² in the n = 3 state.