## Level 3

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

# Illustration **Classically forbidden / allowed region**

## Download

- Vector graphics (SVG) download
*awesome for websites* - Pixel graphics (PNG) download
*awesome for presentations*

**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).