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Unformatted text preview: Physics 137A Fall 2009 Midterm #2 Monday Nov. 16 th 1. (25 points) In each case choose the correct statement: (a) In a region of space where the energy eigenvalue E > V ( x ), the eigenfunction ψ ( x ) is (i) concave towards the xaxis. (ii) concave away from the xaxis. (b) A square potential well in one dimension centered at x = 0 (i) has no bound states if sufficiently narrow or shallow. (ii) always has at least one symmetric bound state, no matter how narrow or shallow. (iii) always has at least one antisymmetric bound state. (iv) always has at least one symmetric and one antisymmetric bound state. (c) Two Hermitian operators R and S commute, implying that (i) R and S have the same eigenvalues. (ii) for any state, (Δ R )(Δ S ) = 0. (iii) states can be found which are eigenstates of both R and S . 2. (25 points) Consider the deltafunction well in one dimension V ( x ) = − αδ ( x ) , where α is some positive constant which measures the “strength” of the potential. This potential hasis some positive constant which measures the “strength” of the potential....
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 Spring '08
 Crommie
 Linear Algebra, Energy, Eigenvalue, eigenvector and eigenspace, pn, antisymmetric bound state

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