# De broglie relationship derivative definition

### De Broglie wavelength (video) | Khan Academy

In , Louis de Broglie, a French physicist, proposed a hypothesis to explain the theory of the atomic structure. By using a series of. Assuming the momentum relationship, however, allowed the derivation of a similar de Broglie relationship for frequency f using the kinetic. The de Broglie hypothesis states that particles of matter can behave as both waves Heisenberg Uncertainty Principle: Definition & Equation.

De Broglie Hypothesis In quantum mechanics, matter is believed to behave both like a particle and a wave at the sub-microscopic level.

The particle behavior of matter is obvious. When you look at a table, you think of it like a solid, stationary piece of matter with a fixed location.

At this macroscopic scale, this holds true. But when we zoom into the subatomic level, things begin to get more complicated, and matter doesn't always exhibit the particle behavior that we expect.

This non-particle behavior of matter was first proposed inby Louis de Broglie, a French physicist. In his PhD thesis, he proposed that particles also have wave-like properties.

## De Broglie wavelength

That makes sense, intuitively. In fact, when thinking about how the energy, or the momentum, affects the shape of the wavefunction, I am reminded of an airplane propeller: The difference is much more fundamental, however: Having said that, the mathematical similarity makes one think!

Of course, you should remind yourself of what E and B stand for: Nevertheless, as mentioned above, the visuals make one think and, as such, do help us as we try to understand all of this in a more intuitive way. We then super-impose the various wave equations to get a wave function that might—or might not—resemble something like this: The energy of a particle is generally thought of to consist of three parts: Imagine two different regions in space that differ in potential—because the field has a larger or smaller magnitude there, or points in a different direction, or whatever: Now, the different potential will change the momentum: Because of the energy conservation principle—or its equivalent in quantum mechanics, I should say: We could work with that: This is rather weird—at first, at least.

So… Well… Just remember: If we do that, we can derive some funny new relationships. We can do that. How do we interpret this? I am not sure. Free space is free space: So people knew about this. And de Broglie suggested, hypothesized, that maybe the same relationship works for these matter particles like electrons, or protons, or neutrons, or things that we thought were particles, maybe they also can have a wavelength.

And you still might not be satisfied, you might be like, "What, what does that even mean, "that a particle can have a wavelength?

### Matter wave - Wikipedia

How would you even test that? Well, you'd test it the same way you test whether photons and light can have a wavelength. You subject them to an experiment that would expose the wave-like properties, i. So, if light can exhibit wave-like behavior when we shoot it through a double slit, then the electrons, if they also have a wavelength and wave-like behavior, they should also demonstrate wave-like behavior when we shoot them through the double slit.

And that's what people did. There was an experiment by Davisson and Germer, they took electrons, they shot them through a double slit.

If the electrons just created two bright electron splotches right behind the holes, you would've known that, "Okay, that's not wave-like. Davisson and Germer did this experiment, and it's a little harder, the wavelength of these electrons are really small.

So you've gotta use atomic structure to create this double slit. It's difficult, you should look it up, it's interesting. People still use this, it's called electron diffraction. But long story short, they did the experiment. They shot electrons through here, guess what they got? They got wave-like behavior.

Simplest derivation of de-broglie's equation.

They got this diffraction pattern on the other side. And when they discovered that, de Broglie won his Nobel Prize, 'cause it showed that he was right. Matter particles can have wavelength, and they can exhibit wave-like behavior, just like light can, which was a beautiful synthesis between two separate realms of physics, matter and light.

### de Broglie relation | Reading Feynman

Turns out they weren't so different after all. Now, sometimes, de Broglie is given sort of a bum rap. People say, "Wait a minute, all he did "was take this equation that people already knew about, "and just restate it for matter particles?

If you go back and look at his paper, I suggest you do, he did a lot more than that. The paper's impressive, it's an impressive paper, and it's written beautifully. He did much more than this, but this is sort of the thing people most readily recognize him for. And to emphasize the importance of this, before this point, people had lots of ideas and formulas in quantum mechanics that they didn't completely understand.

After this point, after this pivot, where we started to view matter particles as being waves, previous formulas that worked, for reasons we didn't understand, could now be proven.