What's the (Electron) Frequency, Kenneth?

[gareththegeek]

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).

 

[f95toli]

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").

 

[gareththegeek]

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?

 

[f95toli]

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.