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
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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).