What's the (Electron) Frequency, Kenneth?

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    Electron Frequency
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SUMMARY

The discussion centers on the frequency of an electron in a ground state hydrogen atom, specifically addressing the misconception that electrons possess a frequency in a bound state. The participants clarify that the energy of 13.6 eV is the ionization energy, not the energy associated with a frequency. They emphasize that while de Broglie's hypothesis of wave-particle duality is foundational, modern quantum mechanics describes electrons using wavefunctions, which do not have a frequency in the classical sense. The conversation concludes with a detailed explanation of the Bohr model and the nature of wavefunctions in quantum mechanics.

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  • Understanding of quantum mechanics principles, particularly wave-particle duality.
  • Familiarity with the Bohr model of the hydrogen atom.
  • Knowledge of wavefunctions and their role in quantum mechanics.
  • Basic grasp of energy quantization and the concept of eigenstates.
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  • Study the derivation and implications of the Bohr radius in hydrogen atoms.
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  • Explore the concept of eigenstates and their time-independent solutions.
  • Investigate the historical context and evolution of quantum mechanics, focusing on de Broglie's contributions.
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Students and professionals in physics, particularly those interested in quantum mechanics, atomic theory, and the foundational concepts of wave-particle duality.

  • #31
f95toli said:
it is not until we take the absolute value of the wavefunction squared that we get "real" (or at least measurable) properties of the system. When you do this here the phase -and all time dependence- disappears.

The squared value of the wavefunction represents a particular measurement and a measurement must be taken at a certain time, so wouldn't the time dependence be implied? The measurement shows the state of the system at a given time, reducing the probability of any other (mutually exclusive) state to zero.

Is this correct? (I am sorry if I am being slow. I am trying my utmost to understand all that is said here and it is a little complicated ;p).
 
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  • #32
gareththegeek said:
The squared value of the wavefunction represents a particular measurement and a measurement must be taken at a certain time, so wouldn't the time dependence be implied? The measurement shows the state of the system at a given time, reducing the probability of any other (mutually exclusive) state to zero.

Is this correct? (I am sorry if I am being slow. I am trying my utmost to understand all that is said here and it is a little complicated ;p).

No, there is no reference to a particular measurement in the formalism. What you get is simply the expectation value, there is no time dependence.

If you were to e.g. drive the atom with an electromagnetic field you could start to induce transitons between levels, in this case the problem become time-dependent which in turn means that you also get time-dependent expectation values (look up e.g. "Rabi oscillations").
 
  • #33
So do you mean that the expectation value is the probability of that measurement regardless of time because the electron is in a fixed pattern about the nucleus?
 
  • #34
Sort of, but this is a general "feature" of all systems of this type.

The same thing is true in e.g. the artificial quantum wells that are used as semiconductor lasers; the levels are stationary so nothing changes over time, which is why the frequency of the laser is -to first order- constant.
 

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