Question

According to quantum mechanics, what are the required conditions which make the quantum tunnelling (of a given object through a given potential barrier) possible/more probable?

Answer 1

Quantum tunneling is a phenomenon in quantum mechanics where a particle can pass through a potential energy barrier even though it does not possess sufficient energy to overcome the barrier classically. The probability of quantum tunneling depends on several factors:

1. Barrier Width and Height: The narrower and taller the potential energy barrier, the lower the probability of tunneling. A wider and shorter barrier increases the likelihood of tunneling.

2. Particle Energy: The energy of the particle plays a crucial role. If the particle's energy is significantly lower than the height of the potential barrier, classical mechanics would suggest it cannot cross the barrier. However, in quantum mechanics, there is a finite probability of tunneling, even for particles with lower energy.

3. Wave Function: The wave-like nature of particles in quantum mechanics is essential for tunneling. The wave function of the particle extends beyond the barrier, allowing it to tunnel through.

4. Barrier Shape: The shape of the potential energy barrier affects the tunneling probability. Smooth and symmetric barriers facilitate tunneling, while irregular or asymmetric barriers can decrease the probability.

5. Particle Mass: The mass of the particle influences tunneling. Lighter particles have a higher probability of tunneling compared to heavier particles for the same energy.

6. Quantum Coherence: Maintaining quantum coherence is crucial for tunneling. Any interaction or decoherence that disrupts the particle's quantum state can reduce the probability of tunneling.

7. Temperature: Higher temperatures generally decrease the probability of tunneling due to increased thermal energy, which makes it more difficult for particles to maintain coherence.

It's important to note that quantum tunneling is a probabilistic phenomenon. While these factors affect the likelihood of tunneling, they do not guarantee that tunneling will occur in all cases. The probability of tunneling is described by the wave function of the particle and can be calculated using quantum mechanical equations, such as the Schrödinger equation, for the specific system under consideration.