Particles as waves

Yet another step towards the new theory was taken in 1924 by Louis de Broglie, a graduate student at the time at the Sorbonne in Paris. So far we have seen that energies of matter (hydrogen atoms) and light are both quantized, and that light can be shown to behave sometimes as particles. Can particles behave sometimes as waves  

Wavelike behavior, such as interference, depend directly on the wavelength, and it is far from obvious what wavelength you would assign to a hydrogen atom, let alone a macroscopic object such as a baseball. For photons we have 

In addition, classical electromagnetic theory predicts that light waves have momentum given by 

Of course, the definition might not be very useful we could also define the ears of an elephant to be wings, but this would not make elephants fly. What makes this definition interesting is a very simple extension. He also argued that the orbit of an electron around a proton would only be stable if its circumference lit R were an integral number of wavelengths. Thus 

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