Dimensional analysis & Quantum q.

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Hmmmm...

Say I have

And I have in units of , in , in what should i get for ?

I keep getting in , can someone please confirm that?

If I plot my graph with attoJs then my electron wavefunction evolves waaaay fast.

If I have (attoJs), then the wavefunction spreads over tens, possibly hundreds of metres in less than a second!

Is it normal for uncertainties to propagate THAT fast?

[mark_alec]

hbar has the same units as h, which has the units Js, not sure why you have atto (any power should be implemented in the exponent, not the unit).

Due to the units of hbar, the exponent is dimensionless (as it should be), and gives the amplitude of a plane wave at a single point as time evolves. For a free electron, it isn't strange to have it moving hundreds of metres per second, remember that particles can travel close to the speed of light (which is ~3*10^8 m/s).

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Thanks mark

The way I did it was:



Turning into units:











does that make sense?

So to cancel, must also be in

[mark_alec]

Dimensional analysis uses dimensions, not units (so length, rather than metres). However, when you are evaluating a problem using metric units, it is best if you keep all units in the system you wish to use (e.g. for SI, use metres, for CGS, use centimetres). Otherwise your derivation is correct.

[full of electrons]

your answer is right since h-bar = 1.05*10^-34 Js.

Normally, when using dimensional analysis, I always convert everything into SI units, it saves confusion.