What's the (Electron) Frequency, Kenneth?

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    Electron Frequency
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Discussion Overview

The discussion centers around the frequency of an electron in a ground state hydrogen atom, exploring concepts related to quantum mechanics, the Bohr model, and the wave-particle duality of electrons. Participants examine calculations related to energy levels, wavefunctions, and the implications of these ideas on the nature of electrons in atomic orbits.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions the frequency of a ground state hydrogen atom's electron, referencing the energy of 13.6 eV and attempting calculations that lead to an incorrect Bohr radius.
  • Another participant clarifies that 13.6 eV is the energy required to free the electron from its orbit, suggesting that the rest energy of the electron is much higher.
  • A different participant asserts that electrons do not have frequencies, challenging the premise of the original question.
  • Some participants discuss de Broglie's hypothesis of wave-particle duality, noting that while it was foundational, modern interpretations suggest limitations in applying classical concepts to quantum particles.
  • There is a discussion about the wavefunction being a probability field and whether it can be associated with a frequency, with some arguing that the wavefunction does not imply oscillation or frequency in bound states.
  • One participant attempts to derive the Bohr radius using de Broglie's wavelength and circular orbit properties, leading to a discussion about the implications of this model.
  • Another participant highlights that if the electron were to behave as described in classical terms, it would emit radiation and spiral into the nucleus, which does not occur.
  • There is a debate about the meaning of frequency in relation to the wavefunction, with some arguing that while the phase has time dependence, it does not imply a measurable frequency in the context of a static wavefunction.

Areas of Agreement / Disagreement

Participants express differing views on the nature of electrons, the validity of classical analogies in quantum mechanics, and the interpretation of wavefunctions. No consensus is reached regarding the original question about electron frequency.

Contextual Notes

Participants note limitations in their calculations and assumptions, particularly regarding the application of equations for massless particles to massive particles like electrons. The discussion also highlights the complexity of quantum mechanics and the evolving understanding of electron behavior.

Who May Find This Useful

This discussion may be of interest to students and enthusiasts of quantum mechanics, particularly those exploring the foundational concepts of atomic structure and 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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