# No free particle in real world

## Main Question or Discussion Point

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" ?

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ZapperZ
Staff Emeritus
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.

jtbell
Mentor
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.

Meir Achuz