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Re: atomic units

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  • Subject: [mg656] Re: [mg627] atomic units
  • From: wmm at (Martin McClain)
  • Date: Fri, 7 Apr 95 15:16:39 EDT

Dear Dale:
There are many times when you need to work with atomic sized quantities in
SI units; usually, in my experience, when you need to think about electric
field perturbations of molecules created in a lab in SI units like volt per
meter, or optical perturbations measured in watt/meter^2.  So the problem
can't always be avoided.  One of the beauties of Mma is that it usually
handles this quite automatically, so that one does not need to go into
specialized units systems designed to get around numerical accuracy limits.

To put my Mma question in a simpler form:  How do you inactivate the
mechanism inside Mma which causes the transformation

In[4]:=         Sqrt[8]
Out[4]=         2 Sqrt[2]

I.e., perfect squares sometimes seem to be located and pulled out of roots
automatically.  This is often useful no doubt, but in the example I gave it
is anti-useful.  How do I turn it off?

Thx-  Martin

>>In solving scientific problems you often run across expressions like
>>xSolns = Solve[2.*10^-25 y==3.*10^-25 x^2+7.*10^-26, x]
>>where the large exponents are generated by the SI unit system applied to
>>atomic scale quantities.  Using Solve, and extracting the answer, the
>>positive solution comes out as
>One solution is to use atomic units.  Then all the coefficients will be
>much more reasonably sized.
>Atomic units are based on the Bohr model of the atom (centrifugal
>force balances Coulomb attraction, and angular momentum is quantized
>in units of hbar).  The unit of length is the Bohr ( a = hbar^2/(m
>e^2) = 0.5297 Angstrom), the unit of energy is the Hartree (E = m
>e^4/hbar^2 = 4.355 10^(-18) Joule), the unit of velocity is v= hbar/(m
>a) = 2.186 10^6 meter/sec, the unit of time is a/v = 2.423 10^(-17)
>sec, and the unit of electric field is e/a^2 = 5.132 10^11
>I realize this "answer" doesn't directly answer your question, but
>atomic units are good to know about.
>Dale Fried
>MIT room 13-2061		|	dgf at
>77 Massachusetts Ave		|	617-253-4863
>Cambridge, MA 02139		|

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