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lnxpy / mdb-ai-prompted-text

MindsDB (mdb.ai) AI Single-prompting Text Using PyAction
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AI: Text Prompting #9

Closed lnxpy closed 2 months ago

lnxpy commented 2 months ago

Text

To illustrate quantum tunneling, consider a ball rolling along a surface with a kinetic energy of 100 J. As the ball rolls, it encounters a hill. The potential energy of the ball placed atop the hill is 10 J. Therefore, the ball (with 100 J of kinetic energy) easily rolls over the hill and continues on. In classical mechanics, the probability that the ball passes over the hill is exactly 1—it makes it over every time. If, however, the height of the hill is increased—a ball placed atop the hill has a potential energy of 200 J—the ball proceeds only part of the way up the hill, stops, and returns in the direction it came. The total energy of the ball is converted entirely into potential energy before it can reach the top of the hill. We do not expect, even after repeated attempts, for the 100-J ball to ever be found beyond the hill. Therefore, the probability that the ball passes over the hill is exactly 0, and probability it is turned back or “reflected” by the hill is exactly 1. The ball never makes it over the hill. The existence of the ball beyond the hill is an impossibility or “energetically forbidden.”

However, according to quantum mechanics, the ball has a wave function and this function is defined over all space. The wave function may be highly localized, but there is always a chance that as the ball encounters the hill, the ball will suddenly be found beyond it. Indeed, this probability is appreciable if the “wave packet” of the ball is wider than the barrier.

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github-actions[bot] commented 2 months ago

Thank you for providing an interesting explanation illustrating quantum tunneling using the analogy of a ball rolling over a hill. In quantum mechanics, particles like electrons can exhibit tunneling behavior where they can pass through energy barriers that would be impassable according to classical mechanics. This phenomenon is a key concept in understanding the behavior of particles at the quantum level. If you have any questions or would like further information on quantum tunneling or any related topics, feel free to ask!