Wave–particle duality theory question

In summary, the conversation discusses the concept of matter waves and de Broglie relations, and the significance of the amplitude in matter waves. It also delves into the wave-particle duality and the probability of finding an electron along its trajectory. The conversation also touches on the limitations and applications of Schrodinger's equations and the Heisenberg uncertainty principle for both photons and electrons. It is suggested to read the Marcella paper for a better understanding of these concepts.
  • #1
tiredryan
51
0
Note this is more of a coursework understanding question rather than a specific homework question.

Homework Statement



I have been reading about matter waves and de Broglie relations which suggest that electrons can act as waves. From wikipedia (http://en.wikipedia.org/wiki/Matter_wave) it suggests that the following is true.
[tex]\lambda = \frac{h}{p}[/tex] and [tex]f = \frac{E}{h}[/tex]
In that article it does not suggest the significance of the amplitude in the matter wave. From the wave–particle duality article (http://en.wikipedia.org/wiki/Wave–particle_duality) it suggests that "upon measuring the location of the particle, the wave-function will randomly "collapse" to a sharply peaked function at some location, with the likelihood of any particular location equal to the squared amplitude of the wave-function there."

The Attempt at a Solution


If I understand this correctly, the probability of finding an ejected electron along a linear trajectory is not equal along its path, but rather the probability is sinusoidal. At one part of the trajectory, I might have a 100% chance of finding an electron when the amplitude is max and [tex]\lambda [/tex]/4 away there is a 0% chance of finding an electron when the amplitude is zero. This is counterintuitive so I want to check if my reasoning is correct.

Thanks in advance.

PS: For a numerical example, solving the equations for an electron in a 10 kV scanning electron microscope yields a wavelength of 12.3 x 10^-12 m (12.3 pm) as from http://en.wikipedia.org/wiki/Electron_diffraction. If I understand this correctly, as an electron travels in this setup, the probability of finding the electron varies from 0% to 100% sinusoidally with a wavelength of 12.3 x 10^-12 m (12.3 pm).
 
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  • #2
So I came across another post in which it describes the photon wave function.
https://www.physicsforums.com/showthread.php?t=8698

In that post, arcnets, stated that "I mean it in the following sense: "It's not possible to define any photon wavefunction from which a probability amplitude for spatial localization can be calculated". (Landau-Lifschitz IV, chapter 1, §4.)"

If I understand this correctly, the probability of a photon at any position cannot be determined. However, the probability of an electron at a position can be determined by Schrodinger's equation. Is this correct?

Thanks in advance.
 
  • #3
So on a related note I have delved deeper into Schrodinger's equations and came across Heisenberg's uncertainty principle. It seems that Schrodinger's equation applys only to electrons and not photons whereas Heisenberg's uncertainty principle apply to photons and electrons. Are these correct limitations to these theories?

Thanks in advance.


tiredryan said:
So I came across another post in which it describes the photon wave function.
https://www.physicsforums.com/showthread.php?t=8698

In that post, arcnets, stated that "I mean it in the following sense: "It's not possible to define any photon wavefunction from which a probability amplitude for spatial localization can be calculated". (Landau-Lifschitz IV, chapter 1, §4.)"

If I understand this correctly, the probability of a photon at any position cannot be determined. However, the probability of an electron at a position can be determined by Schrodinger's equation. Is this correct?

Thanks in advance.
 
  • #4
tiredryan said:
So on a related note I have delved deeper into Schrodinger's equations and came across Heisenberg's uncertainty principle. It seems that Schrodinger's equation applys only to electrons and not photons whereas Heisenberg's uncertainty principle apply to photons and electrons. Are these correct limitations to these theories?

Thanks in advance.

This is totally false. Read the Marcella paper (i.e. don't just read Wikipedia)

http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

Zz.
 
  • #5
Thanks for your quick response. I am a new student to physics, and I am still in my introductory physics class. I am trying to understand the paper and your statement, "this is totally false."

From the paper's statement, "because position and momentum are non-commuting observables, a particle passing through slits always has an uncertainty in its y-component of momentum," I am guessing that my statement, "Heisenberg's uncertainty principle applies to photons and electrons," is correct. Or is it false?

I am guessing that the "totally false" statement has to deal with my other statement on Schrodinger's equation. If I understand the paper correctly, then Marcella was able to determine the "calculation for the probability amplitude and its corresponding probability function" using Schrodinger's equations. I am guessing this would mean that Schrodinger's equations applies to both photons and electrons. Correct me if I am wrong here.

Also is this quote by Arcnet citing Landau-Lifschitz posted earlier false? Arcnets, stated that "I mean it in the following sense: "It's not possible to define any photon wavefunction from which a probability amplitude for spatial localization can be calculated". (Landau-Lifschitz IV, chapter 1, §4.)"
https://www.physicsforums.com/showthread.php?t=8698

Thanks for your response. I'm sorry for my confusion.

ZapperZ said:
This is totally false. Read the Marcella paper (i.e. don't just read Wikipedia)

http://arxiv.org/ftp/quant-ph/papers/0703/0703126.pdf

Zz.
 
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1. What is wave-particle duality theory?

Wave-particle duality theory is a concept in quantum mechanics that states that particles can exhibit both wave-like and particle-like behavior. This means that they can have properties of both waves, such as wavelength and interference, and particles, such as mass and momentum.

2. Who discovered wave-particle duality?

The concept of wave-particle duality was first introduced by physicist Louis de Broglie in 1924. He proposed that all matter, including particles like electrons, could have wave-like properties. This was later supported by experimental evidence from scientists like Davisson and Germer.

3. How does wave-particle duality affect our understanding of the universe?

Wave-particle duality challenges classical physics and our understanding of the universe at a fundamental level. It suggests that the behavior of particles cannot be fully explained by classical laws and that our perception of reality may be limited. It also plays a crucial role in the development of quantum mechanics and has led to many groundbreaking discoveries in science and technology.

4. Can we observe both wave and particle behavior in a single experiment?

Yes, experiments have shown that particles can behave as both waves and particles simultaneously. For example, the famous double-slit experiment demonstrated that photons could exhibit interference patterns like waves, but also behave as discrete particles when observed. This duality is a fundamental aspect of quantum mechanics and has been observed with various particles, such as electrons and even large molecules.

5. How does wave-particle duality impact technology?

Wave-particle duality has had a significant impact on technology, particularly in the development of quantum computing and communication. It has also led to the invention of devices like the scanning tunneling microscope, which uses the wave-like behavior of electrons to image surfaces at the atomic level. Understanding wave-particle duality has also led to advances in fields such as medicine, energy, and materials science.

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