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Unformatted text preview: 8. Libo±, problem 5.23, p. 132. 9. (5 points) Libo±, problem 5.30, p. 143. 10. (5 points) Libo±, problem 5.52, p. 150. 11. Libo±, problem 5.53, p. 151. 12. (20 points) A harmonic oscillator in two dimensions can be written H = H 1 + H 2 where H i = p 2 i 2 m + 1 2 mω 2 x 2 i . The angular momentum L = r × p is L = x 1 p 2x 2 p 1 . Defne A = 1 2 ω ( H 1H 2 ) (1) B = 1 2 L (2) C =i [ A, B ] / ¯ h. (3) (a) Give the explicit Form oF the operator C . (b) Show that A , B , C , H are Hermitian operators. (c) Show that the set A, B, C are closed under commutation, i.e., [ A, C ] = λ 1 B [ B, C ] = λ 2 A where λ 1 and λ 2 are constants. (d) Show that A, B, C each commute with H ....
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 Spring '09
 Work, Harshad number, Liboff

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