I Is it possible to explain Quantum tunneling with the HUP?

[Nam Jeong Woo]

TL;DR Summary

Quantum tunneling with time-energy uncertainty principle

I'm a student in South Korea(It is my first English question ever). I found descriptions of quantum tunneling explained by the uncertainty principle in Korea. There are two kinds of descriptions to explain quantum tunneling; position-momentum and time-energy uncertainty principle.

First, position-momentum uncertainty principle. When two protons collide, the uncertainty of momentum is decreasing, so the uncertainty of position is increasing. Therefore, it is possible to exist the probability of discovery in potential barrier <- is it the right description?

Second, time-energy uncertainty principle. Classically hydrogen needs more than 100 million degrees of temperature for nuclear fusion, but it isn't really the temperature inside the sun, is it? So, we can't go beyond the potential energy, but the time uncertainty is reduced when we look at that time of nuclear fusion, so energy uncertainty is increased and nuclear fusion is possible.

I want to know above all about the second description. These explanations are often found in Korea. But I couldn't find it when I looked it up in English. I wonder whether the explanation is correct.

Is it possible to explain quantum tunneling with the uncertainty principle?

 

[Nugatory]

Is it possible to explain quantum tunneling with the uncertainty principle?

Possible, yes, and that's one of the more common ways of explaining the tunnelling to a non-specialist. It's not exactly wrong, but it is an oversimplification of a more interesting and complete mathematical formuation of the theory.

Classically hydrogen needs more than 100 million degrees of temperature for nuclear fusion, but it isn't really the temperature inside the sun, is it? So, we can't go beyond the potential energy, but the time uncertainty is reduced when we look at that time of nuclear fusion, so energy uncertainty is increased and nuclear fusion is possible.

There are multiple different fusion reactions requiring different combinations of temperature and pressure, so a blanket statement like "needs more than 100 million degrees" is misleading. You don't really need to involve quantum mechaics to understand what's going on inside a star unless you're going to be making detailed quantitative calculations of reaction cross-sections, and that's more than most non-specialists are interested in.

 

[Nam Jeong Woo]

Thank you for your answer. But I can't understand the time-energy uncertainty principle. Some people said 'You should not interpret the time-energy uncertainty principle like the position-momentum uncertainty principle.' I don't know why I should not interpret so on. What are the differences between time-energy and position-momentum?

I interpret the quantum tunneling with the time-energy uncertainty principle as written in the above.
(Wave can't go beyond the potential energy(if the wave doesn't have the energy that crosses the potential barrier), but the time uncertainty is reduced when we look at that time when the wave close to the potential barrier, so energy uncertainty is increased and the wave can cross the barrier. )
But I can't be sure about this explanation because I don't know how to interpret the time-energy uncertainty principle. Is it okay to interpret the T-E as the P-M uncertainty principle?

 

[haushofer]

Griffiths' textbook on QM explains this well in chapter 3.

Basically, the HUP is a general statement about operators. "Time" is not an operator in QM. So the Delta t resembles something else (the time it takes for the energy to change with one standard deviation).