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In quantum mechanics, there exist reflectionless potentials, i.e. potentials whose transmission coefficient is one regardless of the incoming energy.

For a classical wave, such as a wave on a string, one could imagine creating a 'potential' by adding a term to the wave equation, $$\frac{\partial^2 y}{\partial t^2} = v^2 \frac{\partial^2 y}{\partial^2 x} + k(x)y.$$ Physically, this would correspond to attaching the string to vertical springs with strength proportional to $k(x)$. Do there exist reflectionless potentials for this problem?

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  • $\begingroup$ The closest I can think of is noise cancellation but I don't think that's the same. $\endgroup$ – Bill Alsept May 24 '17 at 21:30

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