# IllustrationClassically forbidden / allowed region

Level 3
Level 3 requires the basics of vector calculus, differential and integral calculus. Suitable for undergraduates and high school students.

Share — copy and redistribute the material in any medium or format

Adapt — remix, transform, and build upon the material for any purpose, even commercially.

Sharing and adapting of the illustration is allowed with indication of the link to the illustration.

Harmonic potential energy function $$W_{\text{pot}}(x)$$ with sketched total energy $$W$$ of a particle. Classically the particle always has a positive kinetic energy:$W_{\text{kin}} ~=~ (W_{\text{pot}} - W) > 0$Here the particle can only move between the turning points $$x_1$$ and $$x_2$$, which are determined by the total energy $$W$$ (horizontal line). It is the classically allowed region (blue).

Negative kinetic energy is not physically possible:$W_{\text{kin}} ~=~ (W_{\text{pot}} - W) < 0$

It is the classically forbidden region (red).