De Broglie wavelength of slow moving macroscopic objects

Question

I've seen numerous examples where the De Broglie wavelengths of macroscopic objects such as bullets and baseballs have been calculated. However, in each case, the objects are moving fast and the corresponding momentums are large, resulting in tiny De Broglie wavelengths. What happens if you slow the bullet down to almost a stop. It's momentum is now small, so why doesn't it have a measurable wavelength?

Answer 1

$\lambda = h/p$, where $\lambda$ is wavelength, $h$ is Planck's constant, and $p$ is momentum.

$h = 6.626 \times 10^{-34} Js$

So yes, if you have an object that is moving slow enough, it would have a long wavelength, but the object would have to be essentially not moving to have a momentum on the order of Planck's constant.

What kind of experiment would be able to observe a wavelength in such a situation? De Broglie wavelength is usually observed by interference experiments.

In Quantum Interference of Large Organic Molecules 1 picometer De Broglie waves were observed for 6 nanometer particles moving at 63 m/s. This seems to be the experimental limit for the moment.

Answer 2

No matter how much you slow down the object, at the molecular level, it is going to have particles whizzing around at high speeds.

Answer 3

Building on DavePhD's answer, you need to have some sort of experiment in order to measure/resolve such a length, and this would be done with an interference experiment. In order to have any meaning, the object you are trying to interfere must as least plausibly fit through the slits in the first place. Just looking at order of magnitude estimates, to get something on the order of $\sim 10 $ cm for a 1.0 kg object:

$ v = \frac{h}{m \lambda} \sim 10^{-26}$ feet/hour

That is incredibly slow to the extent that you won't even be sure if the object is moving.

As a general rule of thumb, if you start applying quantum mechanics in such a way to macroscopic objects you will in general get ridiculous results like this that don't really have any meaning.

Answer 4

If I am walking at a constant 1 mph next to a train that slowly accelerates (in its frame of reference) from 0 to 2 mph, I will measure its velocity changing from -1 to +1 mph, so there is an instant when the velocity is zero. At some instant very very close to the zero velocity instant, the train's momentum is much smaller than Plank's constant and the train's wavelength is huge. It is a fleeting instant, but I can choose a very very small relative acceleration than the period of a large matter wave could be as long as I like.