The potential energy inside the potential well for a particle in the potential well problem is typically taken as zero within the well region. This is a common idealization, especially in the infinite potential well (or infinite square well) model, where the potential energy V(x)V(x)V(x) is defined as:
- V(x)=0V(x)=0V(x)=0 inside the well (for 0<x<L0<x<L0<x<L, where LLL is the width of the well),
- V(x)=∞V(x)=\infty V(x)=∞ outside the well (for x≤0x\leq 0x≤0 or x≥Lx\geq Lx≥L),
This means the particle is free to move inside the well with zero potential energy but cannot exist outside the well because of infinite potential barriers
. In more general finite potential well problems, the potential energy inside the well is a constant (often set to zero for convenience), and outside the well, it is some finite positive value V0V_0V0. The particle is thus "trapped" in a region of lower potential energy surrounded by higher potential energy barriers
. To summarize:
- Inside the well: Potential energy V=0V=0V=0 (or a constant reference level),
- Outside the well: Potential energy V=∞V=\infty V=∞ (infinite well) or V=V0V=V_0V=V0 (finite well).
This setup allows the particle to have quantized energy levels due to boundary conditions imposed by the well walls, with the total energy inside the well being primarily kinetic energy since potential energy is zero there
. Hence, the potential energy inside the potential well is usually taken as zero or a constant minimum value, defining the "bottom" of the well where the particle is confined.
