"Tails" & "Bodies of Wave-Functions ?

Please ponder the SWE, for the Hydrogen atom:

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 < r_Bohr,n) -- Q-KE is positive; wave-function is 'concave down'; "body"
  
• Classically-forbidden region (r > r_Bohr,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 ??