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Unformatted text preview: Quantum Mechanics I, Physics 3143: Quiz 2, Fall 2009 1 . (a) What is the inner product ( ψ | φ ) on the complex vector space C N of N × 1 column matrices, | ψ ) → ψ 1 ψ 2 ...... ψ N ? (b) A hermitian operator ˆ A satisfies ( ˆ Aφ | ψ ) = ( φ | ˆ Aψ ) . 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 Schr¨odinger’s energy eigenvalue equation for 0 ≤ x ≤ a/ 2 and a/ 2 ≤ x ≤ a , which have energy eigenfunction ψ ( x ) = 0 for x = 0 and x = a ?...
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This note was uploaded on 01/22/2012 for the course PHYS 3143 taught by Professor Kennedy during the Fall '10 term at Georgia Tech.
- Fall '10