In double slit experiment only small sized particles were used. however if we use large objects such as a tennis ball, the expected pattern is not observed.
Why the wave nature is not visible for large objects in double slit experiment ?
How do I then prove that large objects also have wave nature?
The difficult bit is creating a coherent beam of large objects since the rate of decoherence increases rapidly with the size of the object. If you could create a coherent beam of tennis balls you could diffract it, but in the real world you wouldn't be able to maintain the coherence for longer than the tiniest fraction of a second. As far as I know the largest object that has been diffracted is a buckyball.
It's unlikely you'll ever be able to prove that objects the size of a tennis ball have wave like properties. However since QM correctly predicts diffraction for sizes ranging from electrons to buckyballs there's no obvious reason why this should break down for larger objects.
For more on this subject see the questions:
Will a football (soccer) diffract?
Validity of naively computing the de Broglie wavelength of a macroscopic object
Why doesn't a marble rolling on a table ever reflect back at the edge?
Take the Wave-Particle duality principle and the de Broglie wavelength equation: $$ E = h\nu = \frac{hc}{\lambda}=mc^{2} $$
The Energy of a particle is described by Planck's Constant times the frequency of a particle, or the same constant times the speed of light over the particle's wavelength. Typically we have the energy so we solve for the frequency and inversely the wavelength, where if the wavelength is larger than the slit, the wave won't be able to propagate through the slit. Now the $ mc^2 = \frac{hc}{\lambda} $ equation is the one we want to look at. More specifically, we want to rearrange it so that we can analyze the wavelength of objects of various mass. We obtain: $$ \lambda = \frac{h}{mc} $$ This wavelength is roughly the distance that quantum effect around an object can be observed. For a low mass electron, this yields wavelengths on the atomic scale of distance. Since the electron is that small anyways, we can see the effects of QM pretty well with respect to it.
Now take a human with any mass, you'll come up with a massive energy value, and a correspondingly tiny wavelength. I weight 54 $kg$, and for me that corresponds to a de Broglie Wavelegnth of $ 4.09 \times 10^{-44} \;m $. Cube that, and that's the volume I'd have to be scaled to to observe any quantum effects for my mass. I'd for sure be a black hole before I would observe quantum effects.
By the logic above, large objects will not exhibit wave-like nature. This is why you don't see people popping in and out of existence at different places and times. One could arguably model our entire body as a collection of individual particles, and say the wave-pattern the is found is the sum of all the wave patterns that make us up ( superposition principle ), but doing so ( by actually calculating out the probabilities of you being one place one instant, and in one place in another ) you would find that it is highly improbable--borderline impossible--for every particle in your body to probabilistically appear in the same spot locally, but overall in a different global position over a negligible time ( analogous for the "popping" and "whizzing" in an out of a bar animation ).
For large particles, the wavelength is small and is focused to one direction. So,the two waves don't show any noticeable overlap and hence the absence of interference pattern.
The intensity of the double slits is given by $$I_{\theta} = I_m (\cos \beta)^2 \left( \frac{\sin{\alpha}}\alpha \right)^2$$ where $$\alpha = \frac{\pi a}{\lambda}\sin \theta$$ $$\beta = \frac{\pi d}{\lambda} \sin \theta$$ where $d$ is the distance between the centerlines of the slits and $a$ is the width of each slits.
From this equation, we can work out that for smaller $\lambda$, the wavelength is less spread out.
To understand better, Look at this interactive graph:
https://pbphysics.blogspot.com/2022/09/why-large-particles-dont-show.html#simulation
Since the mass of a tennis ball is large compared that of an electron, its wavelength is very small according to the de-broglie equation. So the interference pattern is, as you can see from the graph, two large peaks directly in front of the slits.
