Frequency of a particle? Frequency of what?

In summary, the conversation discusses the concept of particle-wave duality in quantum physics. The frequency of a particle is defined as the number of cycles per second, but it is unclear what those cycles are measuring. The conversation also mentions the de Broglie relationship and how a particle can be described by a wave-function. There is some confusion about the spatial variation in the probability density, and the conversation ends with some clarification on this topic.
  • #1
WraithM
32
0
Okay, I have a quantum physics problem set, and I would really like to have a clear understanding of what I'm doing before I get into the thick of it.

This is probably incredibly cliche, but I'm having trouble understanding particle-wave duality. I have no problem with the concept of a particle exhibiting wave-like features; however my teacher and textbook are very ambiguous about the frequency and wavelength of particles.

I have no problem with the fact that a photon, an electron, or whatever have frequency, considering that different colors exist :D and other such examples. I'm just not exactly clear on what exactly the frequency is measuring.

So, frequency is defined as the number of cycles per second. My question is in relation to particles "cycles of what?"

So, a wave (as in, ones found at the beach) frequency is measured by number of waves that go by per second. Sound is measuring change in pressure. (I appologize for poor use of words, but please try to understand what I'm getting at.) Then when I get to particles, frequency of a particle is... uh... what?

As I said, I have no problem with the fact that frequency of a particle exists. I have a problem with exactly what the frequency is measuring. Frequency of a particle is the number of cycles of _______ per second. I'm wondering what goes into that blank spot.

Thank you for considering my question and such, I know it probably seems silly, but I honestly can't find a straight answer for this question.

-Matt Wraith
 
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  • #2
The peaks are in the probability distribution of where you are likely to find the particle if you measure its position. Only if you know the momentum perfectly, and thus have maximum uncertainty about the position, will the distribution look like a plane wave where the peaks are equal in size in all directions off to infinity (each possible momentum corresponds to a unique frequency for any given particle); if you've localized the position enough so the probability distribution has a "hump" in it, then by fourier analysis this can be treated as the sum of a lot of plane waves with different possible frequencies, and thus a lot of possible momenta.
 
  • #4
JesseM said:
The peaks are in the probability distribution of where you are likely to find the particle if you measure its position. Only if you know the momentum perfectly, and thus have maximum uncertainty about the position, will the distribution look like a plane wave where the peaks are equal in size in all directions off to infinity (each possible momentum corresponds to a unique frequency for any given particle); if you've localized the position enough so the probability distribution has a "hump" in it, then by fourier analysis this can be treated as the sum of a lot of plane waves with different possible frequencies, and thus a lot of possible momenta.

Careful Jesse; the wavefunction for a given momentum is something like exp[ip.x] --- which has constant modulus over all space and time. Specifically, there is exactly no spatial variation in the probability density. What you've written sounds almost like there is a plane-wave distribution for the probability density, which isn't true.
 
  • #5
genneth said:
Careful Jesse; the wavefunction for a given momentum is something like exp[ip.x] --- which has constant modulus over all space and time. Specifically, there is exactly no spatial variation in the probability density. What you've written sounds almost like there is a plane-wave distribution for the probability density, which isn't true.
Ah, so it's only a spatial variation in the phase? I haven't studied this stuff in a while...
 
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What is frequency in relation to a particle?

Frequency is a measure of how often a particle repeats its motion in a given amount of time. It is typically measured in hertz (Hz) or cycles per second.

How is the frequency of a particle determined?

The frequency of a particle can be determined by measuring how many times it completes a full cycle of motion in a given time period. This can be done using specialized equipment or by observing the particle's behavior over time.

What factors can affect the frequency of a particle?

The frequency of a particle can be affected by various factors such as its mass, speed, and the strength of any forces acting on it. Changes in these factors can cause the frequency to increase or decrease.

Why is the frequency of a particle important to study?

The frequency of a particle is an important factor in understanding its behavior and characteristics. It can also provide valuable information about the forces and interactions affecting the particle.

How does the frequency of a particle relate to other properties, such as wavelength and energy?

The frequency of a particle is directly related to its wavelength and energy. As the frequency increases, the wavelength decreases and the energy increases. This relationship is described by the equation E=hf, where E is energy, h is Planck's constant, and f is frequency.

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