wavefunction linear
In the case in which left and right are symmetric, c is real. By redefining the phase of the wavefunction in time, 



ψ
→
ψ

e

i
2
c
t




{\displaystyle \psi \rightarrow \psi e^{i2ct}}

, the amplitudes for being at different locations are only rescaled, so that the physical situation is unchanged. But this phase rotation introduces a linear term.
