Re: electron


"Bjoern Feuerbacher" <feuerbac@xxxxxxxxxxxxxxxxxxxxxxxx> wrote in message
news:d4r4r9$aoh$1@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
> patrick wrote:
>> ----- Original Message -----
>> From: "Bjoern Feuerbacher" <feuerbac@xxxxxxxxxxxxxxxxxxxxxxxx>
>> Newsgroups: sci.physics
>> Sent: Thursday, April 28, 2005 10:59 AM
>> Subject: Re: electron
>>
>>
>>
>>>patrick wrote:
>>>
>>>[snip]
>>>
>>>
>>>
>>>>Bjoern
>>>>In Beiser Concepts of Modern Physics (an old edition) is done a
>>>>calculation for the electron in Hydrogen atom.
>>>
>>>How? What line of reasoning does he use in the calculation?
>>>
>>>
>>>
>>>>The average x postion is shown to be a constant over time.
>>>
>>>Averaged over what?
>>
>>
>> This is his calculation:
>> Considering only the x coordinate:
>> x_average=Integral{ x PSI PSI*}dx where PSI is the nornmalized wave
>> function.
>
> Does the integral run only over x or over the whole volume? You wrote
> the first, but I suspect it should be the second.
>
> If yes, that's the expectation value of x, in general written as <x>.
>
>
>> For a quantum number n and energy E_n the time dependant wave function
>> PSI_n=psi_n exp{-(2pi iE_n/h)t }.
>> He substitutes PSI_n into x_average and gets
>> x_average=Integral{x PSI_n PSI_n*}dx
>> =Integral{x psi_n psi_n*}dx
>>
>> which is constant since psi_n and psi_n* are functions of position only.
>
> Yes, the expectation value of the position of the electron does not depend
> on time.
>
>
>> The electron does not oscillate and no radiation occurs.So an atom in a
>> specific
>> quatum state does not radiate.
>
> Yes.
>
>
>> He goes on to show how in a jump from E_m to E_n that an atom radiates
>> during the transition at the predicted frequency (E_m-E_n)/h by showing
>> x_average varies with time during the transition.
>>
>> Hence my conclusion of stationary electron.
>
> It's a bad idea to draw conclusions about the behaviour of a
> quantum-mechanical objects merely from the knowledge of an expectation
> value.
>
> The expectation value tells you essentially what you will get when
> you make a lot of measurements and average over them. And a
> time-independent average does not necessarily imply that the individual
> measurements over which was averaged are also independent
> of time.
>
> You can predict things based on expectation values (like the "no
> radiation" statement), but it's not really possible to conclude anything
> directly about the underlying behaviour.
>
>
>
> Bye,
> Bjoern


Ok thanks for all that. I'll get that book Styer.
But will probably put this Beiser point here in a separate to thread later
to see what other people think.

patrick


.

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