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What differs Quantum from classical mechanics is that CM states the electron will never be able to penetrate the potential barrier while QM states there is finite probability the electron will be observed at the other side of the barrier as if nothing happens inside the barrier.

The formula used to calculate the probability is:

[tex]T = e^{-2kL} ~where ~k = \sqrt{\frac{8 \pi^2 m (V_0 - E)}{h^2}}[/tex]

I want to ask several questions:

1. Why an electron can penetrate through the barrier even though it has lower energy compared to the barrier?

2. CM states that if the energy of electron is higher than the barrier, it will definitely passes through while QM states there is finite chance that it will be reflected back. Why does QM states that? Why doesn't the electron behaves just like what CM predicts, penetrating through the barrier when it has higher energy than the barrier?

3. Can we use the same formula to calculate the probability when electron has higher energy compared to the barrier? Or because it is not tunneling (the term "tunneling" only applies when electron has lower energy with respect to the barrier) we can't use the formula (the formula is strictly limited to "tunneling")?

4. If we can't use the same formula, is there other formula used to calculate the transmission probability when electron has higher energy compared to barrier (because in QM the probability of electron passing through barrier is not 100% even though it has higher energy)?

Thanks