sol-mt2 - Physics 137A Fall 2009 Midterm#2 Monday Nov 16 th...

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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 x-axis. (ii) concave away from the x-axis. (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 delta-function 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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sol-mt2 - Physics 137A Fall 2009 Midterm#2 Monday Nov 16 th...

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