# How wide does a door have to be for a cat running through it to interfere with itself? [closed]

A cat runs through a door. Assuming h = 1 J s, mass of the cat is 1 kg, and the velocity of the cat is 1 m/s. Assume the cat is a quantum particle. How wide does this door have to be for the cat to interfere with itself?

I think what I am struggling with most here is the assumption one needs to make. My instinct is telling me to use de Broglie's wavelength:

$$\lambda = \frac{h}{p} = \frac{h}{mv} = \frac{1\,J\,s}{1\,kg\;1\,m/s} = 1\,\mbox{m}$$

But how does one know that this is the width of the door?

## closed as off-topic by John Rennie, Cosmas Zachos, JMac, Jon Custer, GiorgioPMar 5 at 22:27

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• Was the question given with the assumption that h = 1? – JMac Mar 5 at 17:26
• Look up: wave diffraction and interference. – João Vítor G. Lima Mar 5 at 17:27
• Yes, it is testing understanding and logic – hmwphysics Mar 5 at 17:28

## 2 Answers

The Planck constant is $$6.626 × 10^{−34} J s$$. The $$\lambda$$ consequently. In any case the slit should be of the order of magnitude of the wavelength in order to have diffraction. Clearly not applicable to an ordinary macroscopic object.

• The question seems to be a situation where the Planck constant is instead 1, so obviously it falls apart when you use a real Planck constant, but I don't think that's the point. – JMac Mar 5 at 18:38

This is a scaled up version of single slit diffraction.

When a quantum object passes through an opening that is comparable in size to the de Broglie wavelength $$\lambda$$ of said object, diffraction occurs.

From Huygens' principle we can think of the slit as many small slits each being a separate emitter of waves which then interfere with each other. A single slit diffraction pattern can be seen on a screen that is far enough away from the opening.

And so the cat interferes with itself when the door width is comparable to it's de Broglie wavelength.