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## Homework Statement

I must be missing out on some fundamental part of quantum mechanics, since I'm unable to quite grasp the following thought experiment. A 1kg ball is confined in a onedimensional box with a length of 1m. What is it's maximal De Broglie wavelength?

## Homework Equations

[tex]\lambda=h/p[/tex] (De Broglie Hypothesis)

[tex]\Delta x \Delta p \ge \frac{h}{4\pi}[/tex] (Heisenberg uncertainty principle)

## The Attempt at a Solution

So the way i see it, it's maximal de broglie wavelength will occur when the momentum of the ball is at it's minimum. The momentum cannot be precisely determined to be zero since the ball is confined in finite space. Since it's [tex]\Delta x = 1\textrm{m}[/tex], the minimum in momentum will occur at [tex]\Delta p = \frac{h}{4\pi}[/tex].

The wavelength at this momentum is :

[tex]\lambda=\frac{h}{h/(4\pi)}} = 12.57m[/tex]

Now this wavelength is larger than the dimensions of the confining space . Could someone shed some light on this? I'm getting a macroscopically tangible wavelength for an object at a very slow speed. Overall, how should i interpret de broglie wavelengths for objects with an extremely small momentum?

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