Widdekind Posted April 20, 2011 Share Posted April 20, 2011 Please ponder the SWE, for the Hydrogen atom: [math]E \Psi \; = \; \hat{K} \Psi \; + \; V \Psi[/math] where [math]\hat{K} \propto - \nabla^2[/math] is the 'QM KE', or 'Q-KE', operator. Now, the energy [math]E[/math] is a constant. But, the potential energy [math]V[/math] varies through space, being "very negative" near the nucleus, and "nearly zero" far from it. Thus, this leads to two regions, of the Schrodinger solutions, for the Hydrogen wave-functions: Classically-allowed region (r < rBohr,n) -- Q-KE is positive; wave-function is 'concave down'; "body" Classically-forbidden region (r > rBohr,n) -- Q-KE is negative; wave-function is 'concave up'; effervescent exponentially-decaying "tail" Now, what does negative KE mean ? If KE is "stored Work energy", does that mean, that the "tails" of wave-functions can do no Work, on other objects ?? To wit, only the "bodies" of wave-functions resist compression forces, generating the 'structural strength' of some molecular quantum system ?? Link to comment Share on other sites More sharing options...
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