Potential Barrier (Q.M. vs Classical Phy.)

[n0_3sc]

If you have a Potential Barrier V (width a) and particles incident on left with energy E where E>V, are the following true:

Classical Physics:
- All particles will be transmitted past the barrier
- It cannot be reflected because that would mean it has negative E which is not possible.

Quantum Mecahnically:
- Some particles will be reflected (due to there wave nature)
- Some particles will be transmitted
- Some particles may exist in the barrier
- Resonant modes exist for 100% transmission of particles

Am I missing anything important?

 

[LHarriger]

In order:

Classical Physics:
- Yes
- You are correct that it cannot be reflected in the case of E>V but this has nothing to do with negative energy, rather it is reflected if E<V. Moreover, you can have a negative energy if your potential is defined for negative values. (In fact, potentials are often defined such that bound states correspond to negative energies.)

Quantum mechanically:
- Yes
- Yes
- Yes, but only if E<V (the opposite of your stated case) and if your barrier is a well and not a step.
- Not so sure about the resonant modes part.

Now someone else can check to see if I missed anything important.