Finding solutions for combined 1D potentials with scattering states

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morve
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Sketch of a 1D potential V(x) against x: a rectangular barrier rising above zero, and a downward-pointing arrow at a point further right on the x-axis.


Image is a set of 1D potentials which i need more examples and their solutions containing transmitting states, bounded states, scattering states and coefficients.

I searched with

"1D potential combinations"

"1D potential set"

keywords but can not find anything yet.

Which keyword should i use to find solutions of well, barrier, delta combining potentials.

P.S. I know this is off topic but i must ask, thanks