Fall 09 Quiz 2

Fall 09 Quiz 2 - Quantum Mechanics I, Physics 3143: Quiz 2,...

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Unformatted text preview: Quantum Mechanics I, Physics 3143: Quiz 2, Fall 2009 1 . (a) What is the inner product ( | ) on the complex vector space C N of N 1 column matrices, | ) 1 2 ...... N ? (b) A hermitian operator A satisfies ( A | ) = ( | A ) . Which of the following operators are hermitian ? (a) i x + x 2 , on the space of square integrable functions L 2 ( R ). (b) x d dx x , on the space of square integrable functions L 2 ( R ). (c) 1 2 i 1 2 i 1 1 + i 1 1 i i , on the vector space C 3 . 2 . A mass m particle is in a one-dimensional box; inside it a step of height V starts at x = a/ 2. (a) Consider energies E < V . What are the solutions to Schrodingers energy eigenvalue equation for 0 x a/ 2 and a/ 2 x a , which have energy eigenfunction ( x ) = 0 for x = 0 and x = a ?...
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Fall 09 Quiz 2 - Quantum Mechanics I, Physics 3143: Quiz 2,...

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