Particle on the forbidden region

TL;DR

Quantum mechanics evades the problem of measuring particles in the forbidden region by introducing the uncertainty principle.

Transcript

PROFESSOR: We have found in this solution with some energy like this, that there's a decaying exponential over this side. And the question is often asked, well what happens if you tried to measure the particle in the forbidden region? Must be a problem. If you find the particle in the forbidden region, it has energy E that is less than v0, so you y... Read More

Key Insights

• 😘 The forbidden region in quantum mechanics prevents particles with energy lower than a certain threshold from existing.
• 🕵️ Detecting particles in the forbidden region would imply negative kinetic energy, which is not physically possible.
• 🚫 The uncertainty principle introduces momentum uncertainty and prevents the measurement of particles in the forbidden region.

Questions & Answers

Q: What is the forbidden region in quantum mechanics?

The forbidden region in quantum mechanics is a region where particles cannot exist if their energy is less than a certain value. It is governed by an exponential function and has a length scale of about 1 over kappa.

Q: Why is finding a particle in the forbidden region with negative kinetic energy contradictory?

Finding a particle in the forbidden region with negative kinetic energy is contradictory because it would violate the laws of physics. Negative kinetic energy is not physically possible for a particle.

Q: How does the uncertainty principle prevent the measurement of particles in the forbidden region?

The uncertainty principle states that there is a trade-off between position and momentum measurements. When a particle is localized in position, there is uncertainty in its momentum. This uncertainty in momentum results in an uncertainty in kinetic energy, preventing the observation of particles with negative kinetic energy in the forbidden region.

Q: What happens if a particle is detected in the forbidden region?

If a particle is detected in the forbidden region, its total energy will be equal to or greater than the energy threshold of the forbidden region. It will have either zero total energy or normal kinetic energy, without any strangeness or contradiction.

Summary & Key Takeaways

• In quantum mechanics, there exists a forbidden region where particles cannot exist if their energy is less than a certain value.

• If a particle is found in the forbidden region, it would have negative kinetic energy, which seems contradictory.

• The uncertainty principle prevents the measurement of particles in the forbidden region by introducing momentum uncertainty and disallowing negative kinetic energy.