Answers for Assigned Problems

6.2 (a) E_n = (n + 1/2) hbar w sqrt(1+e)
      (b) E_n' = (e/2) (n+1/2) hbar w

6.3

	Ground state	First excited state
y	(2/a) sin (p x1 / a) sin (p x2 / a)	(Ö2 / a) [sin (p x1 / a) sin (2 p x2 / a) + sin (2 p x1 / a) sin (p x2 / a)]
E0	p2 hbar2 / (m a2)	(5/2) p2 hbar2 / (m a2)
E1	(-3/2) V0	-2 V0

6.7 (b) E' = -sqrt(p) (V₀a/L) (1 ± e ^{- (2pna/L)2})
      (c) sqrt(2/L)i sin(2pnx/L), sqrt(2/L) cos(2pnx/L)
      (d) The parity operator, defined by Py(x) = y(-x), whose eigenfunctions are (all) even and odd functions

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Last revised 2005/05/05