hw3246 - 8. Libo, problem 5.23, p. 132. 9. (5 points) Libo,...

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Physics 246, Spring 2007 Homework #3 Due in class, Wednesday, February 21, 2007 Feel free to discuss the problems with me and/or each other. Each student must write up his/her own solutions separately. Each problem is worth 10 points unless otherwise indicated. 1. Libo±, problem 4.15, p. 108. 2. Libo±, problem 4.28, p. 111. 3. Libo±, problem 4.35, p. 114. 4. Libo±, problem 4.36, p. 114. 5. (15 points) Consider a particle of mass m in N dimensions with H = 1 2 m n X i =1 p 2 i + V ( x i ) where V ( x i ) = 0 for all x i for 0 x i a and V ( x i ) = otherwise. (a) What are the energy eigenfunctions and their eigenvalues? (b) What are the six lowest energy eigenvalues (assume N 5)? (c) How many distinct states are there for each of these energies? 6. Libo±, problem 5.2, p. 128. 7. Libo±, problem 5.3, p. 128.
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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 m 2 x 2 i . The angular momentum L = r p is L = x 1 p 2-x 2 p 1 . Defne A = 1 2 ( H 1-H 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 ] = 1 B [ B, C ] = 2 A where 1 and 2 are constants. (d) Show that A, B, C each commute with H ....
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hw3246 - 8. Libo, problem 5.23, p. 132. 9. (5 points) Libo,...

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