# Superposition of potentials

I'm trying to understand what superposition of potentials means.
For example, let be $$V_0(x) = \begin{cases} 0 &x \in [0,2a]\\ +\infty & \text{otherwise}\end{cases}$$ and $$V_1(x)=-\lambda\delta(x-a), \qquad\lambda>0.$$ If I want to determine the superposition between $$V_0$$ and $$V_1$$, what is the result? I thought that it is a simple "union" of the two potentials, so
$$V(x) =V_0(x)+V_1(x)= \begin{cases} -\lambda\delta(x-a) &x \in [0,2a]\\ \\ +\infty & \text{otherwise}\end{cases}$$ Is this correct?

• Are you talking about superposition of states? "superposition of potentials" just sounds like a strange way to say that they are additive. And that has little to do with it being quantum. Maybe you are using the right terms, and I simply have no idea what they mean. But maybe you are using the wrong terms. Jul 9 at 16:24
• I’m sure of what I wrote because I reported an exam text.
– Gyro
Jul 9 at 16:39
• Right. $V_1$ with BCs imposed by $V_0$. People abuse language. Jul 9 at 16:44
• Yes. In the context of it being from an exam test, they most likely meant two additive potentials, but the phrasing of the question "superposition of potentials in quantum mechanics" was misleading. Jul 9 at 16:48