Question

Do classical waves have reflectionless potentials?

Answer 1

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,

∂2y∂t2=v2∂2y∂2x+k(x)y.∂2y∂t2=v2∂2y∂2x+k(x)y.

Physically, this would correspond to attaching the string to vertical springs with strength proportional to k(x)k(x). Do there exist reflectionless potentials for this problem

Answer 2

v2ò + v3ô + v6ö = v11ø

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