Uncertainty particle function evolves over time

In summary, the conversation discusses the measurement of a proton's position with an accuracy of \Deltax = 10^-11 m and the calculation of \Deltax one second later, assuming v << c. The suggested solution involves using the uncertainty principle to calculate the uncertainty in momentum and then multiplying it by time and dividing by mass to determine the change in position after one second.
  • #1
faen
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Homework Statement



The position of a proton is measured with an accuracy of [tex]\Delta[/tex]x = 10^-11 m
Calculate [tex]\Delta[/tex]x one second later. Assume v << c.

Homework Equations



Heisenbergs uncertainty principle perhaps.

The Attempt at a Solution



I assume this requires knowledge about how the particle function evolves over time, but because the function is unknown in this case, its random how it evolves...
 
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  • #2
Thought a bit more about it. If i calculate the uncertainty in momentum by using Heisenbergs uncertainty principle. Then multiply it by t and divide by m, to calculate [tex]\Delta[/tex]x a second after. Does this sound right?
 
  • #3
Add that answer to Delta x.
 

1. What is an uncertainty particle?

An uncertainty particle is a theoretical concept in quantum mechanics that describes the probabilistic nature of subatomic particles. It is used to explain the uncertainty principle, which states that it is impossible to know both the position and momentum of a particle simultaneously.

2. How does the uncertainty particle function evolve over time?

The evolution of the uncertainty particle function is described by the Schrödinger equation, which is a mathematical equation that predicts the probability of finding a particle at a certain location at a specific time. As time passes, the wave function of an uncertainty particle spreads out and becomes more diffuse, representing a greater uncertainty in its position.

3. What factors affect the evolution of the uncertainty particle function?

The evolution of the uncertainty particle function is affected by various factors, such as the initial conditions of the particle, external forces or interactions, and the measurement process. These factors can cause the wave function to collapse and the particle to take on a specific position and momentum.

4. Is the evolution of the uncertainty particle function deterministic or random?

The evolution of the uncertainty particle function is considered to be probabilistic and therefore, inherently unpredictable. While the Schrödinger equation can predict the probability of finding a particle at a specific location, it cannot determine the exact position and momentum of the particle.

5. What implications does the evolution of the uncertainty particle function have in our understanding of the physical world?

The concept of the uncertainty particle and its evolution highlights the limitations of our understanding of the physical world at the subatomic level. It challenges the traditional notions of causality and determinism and sheds light on the probabilistic nature of reality. This has implications for our understanding of the fundamental laws of nature and our perception of the universe.

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