Unformatted text preview: responding eigenvalues. How many solutions are there for every value of Ω ? Is there a possibility for degeneracies? b) Show explicitly that the eigenstates are orthogonal to one another and that they form a complete set; i.e., they are linearly independent, and any state in this twodimensional space can be expressed as a linear combination of 1 Ψ and 2 Ψ . c) Write down the spectral expansion of ˆ H . d) What would happen if Ω were a complex number? (Don’t try to solve the whole problem again. Just explain what this would mean physically and how the eigenstates and eigenvalues might be qualitatively different.)...
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 Fall '08
 Mccall
 Linear Algebra, Electron, Fundamental physics concepts, Hilbert space, Nancy Makri, spectral expansion

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