Is there an intuitive explanation as to why the de Broglie wavelength of a particle (say a photon) is inversely proportional to its momentum? It can be shown, mathematically, that:
$$E = h\dfrac{c}{\lambda}$$ $$E^2=(mc^2)^2+(pc)^2$$ $$E_{\text{photon}}^2 = (pc)^2$$ $$h\dfrac{c}{\lambda} = pc$$ $$\therefore \boxed{\frac{h}{\lambda} = p}$$
However, I fail to conceptually understand why this is the case. Why is $p$ $\propto$ $\dfrac{1}{\lambda}$?
For some context, I'm a high school student with only a superficial understanding of quantum mechanics or calculus, but answers of every level are more than welcome.
