# Physical Representation of the de Broglie wavelength

1. Dec 28, 2004

### Hyperreality

Louis de Broglie hypothesized every particle moving with momentum $$p$$ has a wavelength of

$$\lambda=\frac{h}{p}$$

If I understand it correctly, is the de Broglie wavelength directly related to the wavelength of $$\psi(x)$$? But because according to quantum physics, the particle coexists with the wave packet. But wave packet is the sum of many waves, therefore its wavelength (wave number) has different values at different intervals.

2. Dec 28, 2004

### dextercioby

Yes,a 'de Broglie wave function',solution of the zero potential Schroedinger'e quation is:
$$\Psi(\vec{r},t)=\frac{1}{(2\pi\hbar)^{3/2}} \exp[{-\frac{1}{i\hbar}(\vec{p}\cdot\vec{r}-Et)]$$
,where u can see the substitutions $\vec{p}=\hbar\vec{k};E=\hbar\omega$
Yes,the monocromatic de Broglie plane wave pictured above does not describe the quantum state of a particle as it unnormlizable,that's why we have to consider the quantum state as linear superposition of such waves=>wave packet which has indeed a broad range of wavelengths.

Daniel.

3. Dec 30, 2004

### saiarun

Is the debroglie wave real. i.e, is the electron in the form of a wave or is the wavelength(lamda) just a theoretical value to get the wave function. Can it be thought in the following way : The wavelength( using the wave function) just gives the probability of the existance of the electron in a particular place and nothing to do with the wave property of the electron.

4. Dec 30, 2004

### Staff: Mentor

Define "real".

That wavelength has everything to do with the wave properties of the electron. It determines the characteristics of the interference and diffraction patterns that electron beams produce.

5. Dec 31, 2004

### saiarun

By real waves I mean similar to mechanical waves. De broglie wave doesnt seems to be mechanical wave and just gives the probability of the existance of the electron in a particular place and nothing to do with the wave property of the electron. Am I right or give your sugesstions.

6. Dec 31, 2004

### ppnl2

Mechanical wave in what?

As I understand it the De broglie wave is exactly the same thing as the wave length of a photon except that you have to take into account the mass and velocity to get momentum.

So is the wavelength of light a mechanical wave? What is it waveing?

No it is just a way of finding the probability of finding a particle called a photon in a given place. It is this probability wave like property of photons that make light look like a classical wave. In reality it is neither classical wave nor classical particle. It is a quantum object. Ditto particles with mass like electrons.

7. Dec 31, 2004

### dextercioby

1."Real waves" means that they have physical existance.Mechanical waves are just one sort of waves.EM,waves describing massive particles,mechanical waves,thermal waves,all are just waves.And they exist
2.De Broglie's wave is a very "real" wave,also called probability wave.Wave mechanics invented by Schroedinger doas a wonderful job in explaining quantum behavior of particles by means of De Broglie waves associated to them.
3.If De Broglie wave has nothing to do with the "wave property of the electron",then what does????
4.You're wrong.Read a book on intro to QM without too much math:David J.Griffiths "Introduction to quantum mechanics" is a good place to start.

Daniel.

8. Jan 3, 2005

Recently in a physics lecture, I suggested that the schroedinger function might describe the fluctuation between energy and matter (my lecturer stongly contested this sugestion!). The origin of the thought is that every wave has (should have..)an oscilator. Therefore what is the oscillator in Schrodinger's function?

9. Jan 3, 2005

### misogynisticfeminist

If I'm not wrong, the question "what is oscillating" somewhat dismissed claims that the wavefunction is analogous to a de broglie wave.

Hmmmm but doesn't the more or less, mainstream interpretation of QM says that the wavefunction is just simply a probability distribution and not a physical wave or a "real" wave.

Isn't that right? I may be wrong though.

Last edited: Jan 3, 2005
10. Jan 3, 2005

Not that I am an expert but...
Yes, you are right. But why can't I propose that the wavefunction represents the oscillation between matter and energy. Not that this is necessarily any more meaningful that just calling it a function of probability.

I futhermore suggest that ascribing the oscillation of matter/energy to de Broglie's wave could also (possibly) be appropriate. We could say that that the density of de Broglie's waves for large particles explain why we cannot detect their energetic mode. Small particles spend much more time in the 'energy' mode explaining their wavelike behavior.

I understand that this is not the accepted interpretation, and furthermore, that I may be spouting nonsense. I would just like to know why!

11. Jan 3, 2005

### Staff: Mentor

You can propose anything you like, but don't expect people to pay much attention to it unless you can point to experimental evidence for it, or at least propose a realistic experiment that can test your ideas.

At the moment, it's less meaningful. We can verify the probability distributions by doing experiments, for example by scattering electron beams off of atoms and using the data to plot the probability distributions of atomic electrons. How would we verify the existence of matter/energy oscillations?