What's the (Electron) Frequency, Kenneth?

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The discussion centers on the frequency of an electron in a ground state hydrogen atom, with initial confusion about the energy value of 13.6 eV and its implications for calculating the Bohr radius. Participants clarify that 13.6 eV is the energy required to free the electron from the nucleus, while the correct Bohr radius is approximately 0.05 nm, not the calculated 14.5 nm. The conversation highlights the distinction between wave and particle behavior of electrons, emphasizing that while the wavefunction describes probabilities, it does not have a frequency in the classical sense. The modern understanding of quantum mechanics acknowledges that electrons exhibit both wave-like and particle-like properties, but the wavefunction itself is static in bound states. Overall, the thread underscores the complexities of quantum mechanics and the evolution of concepts from early theories to contemporary interpretations.
  • #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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