Stationary States in 1D where energy E sits relative to two asymptotic potential levels VLV_L and VRV_R

Bound state

E<VL,VRE < V_L, V_R

Reflecting state

VL<E<VRV_L<E<V_R

Scattering state

E>VL,VRE>V_L, V_R

Where

VL=lim⁡x→−∞V(x),VR=lim⁡x→+∞V(x)V_L = \lim_{x \to -\infty} V(x), \qquad V_R = \lim_{x \to +\infty} V(x)