# No free particle in real world

• matness
In summary: For example, in classical mechanics, the displacement field of a particle is a plane wave. This is because the wave equation neatly describes the behavior of a particle at any given point in space. Similarly, the wave function of a free particle is a plane wave because it represents the probability of finding the particle at any given point. However, there are some situations in which the wave function of a free particle cannot be represented by a plane wave. This is the case for a free particle in a closed system, such as the Earth in space.
matness
maybe it is an easy question but i confuse a bit

wave func of free particle is A exp(ikx) and probability over all space is
A^2 so it is possible to find this particle everywhere

Does it mean "there exist no free particle in real world" ?

matness said:
maybe it is an easy question but i confuse a bit

wave func of free particle is A exp(ikx) and probability over all space is
A^2 so it is possible to find this particle everywhere

Does it mean "there exist no free particle in real world" ?

At some point, you have to consider what is "small enough" to no longer be significant, and what is "large enough" to consider it to be edgeless.

On paper, the influence of the gravity from Alpha Centauri is not zero. But it would look silly if all our dynamical description would have to include such things. The same thing with "free electron". Compare to its "size", such as its deBroglie wavelength, there are MANY situation in which the electron has no clue that it has a boundary. In a typical metal, the conduction electron in your tiny wires can be considered as "free" electrons. This is because using such an approximation (called the Drude model), we could obtain practically all the usual properties of a conductor, such as Ohm's Law. When it works this well, it is very difficult to argue that such an assumption is incorrect.

Other situations such as in particle accelerators explicitly considers charged particles/electrons to be free.

Zz.

matness said:
wave func of free particle

...with a completely definite value of momentum $p$, that is, $\Delta p = 0$...

is A exp(ikx)

...where $k = p / \hbar$...

and probability over all space is A^2 so it is possible to find this particle everywhere

...that is, $\Delta x = \infty$.

Does it mean "there exist no free particle in real world" ?

No, it means, "there exist no free particle with $\Delta p = 0$ in the real world." A realistic wave function for a free particle is a wave packet: a superposition of waves with a finite spread $\Delta p$ in momentum, which leads to a finite spatial width $\Delta x$ according to Heisenberg's Uncertainty Principle.

Doing physics means making appropriate approximations.
The plane wave WF is very useful for many of these.

## 1. Why can't we find a completely free particle in the real world?

The concept of a completely free particle is a simplification used in theoretical physics. In reality, all particles are subject to various forces and interactions, making it impossible for them to exist in a completely isolated and free state.

## 2. What are some examples of forces that prevent particles from being completely free?

Some examples of forces and interactions that prevent particles from being completely free include gravity, electromagnetic forces, and nuclear forces. These forces can be caused by other particles, fields, or even the structure of space-time itself.

## 3. How do these forces affect the behavior of particles?

The presence of forces and interactions can alter the trajectory, velocity, and energy of particles. This can lead to phenomena such as particle collisions, particle decay, or the formation of bound systems like atoms and molecules.

## 4. Are there any exceptions to the concept of no free particles in the real world?

Some particles, such as neutrinos, are considered to be nearly free as they have very little interaction with other particles. However, even these particles are subject to some level of interaction and are not completely free in the strictest sense.

## 5. Does the absence of free particles have any practical implications?

The absence of free particles in the real world has significant implications for our understanding of the universe. It helps us explain various phenomena, such as the formation of matter and the behavior of objects on a macroscopic scale. Additionally, it has practical applications in fields such as particle physics and cosmology.

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