Question

For particles incident from the left on the potential energy shown below, what incident energies E would imply a possibility of later being found infinitely far to the right? Does your answer depend on whether the particles behave classically or quantum-mechanically?

Short answer

The answer depends on the nature of particles: Quantum or Classical.

Step-by-step solution

Definition of tunneling

Classically, it is not allowed that a particle with energy less than the energy of a barrier would pass through it but quantum mechanically, it is possible. This phenomenon is called tunneling.

Explanation and conclusion

The solution to any energy greater than U₁ would be sinusoidal. So, in the middle of the barrier to the right side, the transmission would be allowed.

But this would be possible only for a quantum particle. A classical particle would need energy greater than U₂ to get past the barrier.