RE: Re: Physical Constants package

• To: mathgroup at smc.vnet.net
• Subject: [mg46969] RE: [mg46954] Re: Physical Constants package
• From: "David Park" <djmp at earthlink.net>
• Date: Thu, 18 Mar 2004 01:24:54 -0500 (EST)
• Sender: owner-wri-mathgroup at wolfram.com

```Curt,

You may wish to try out the V4ExtendUnits and V4ReducedUnits package at my
web site below. It allows you to install your own units, such as Hartree,
and it allows you to setup reduced unit systems where certain physical
constants are equal to 1 and then freely convert from and to standard units.

But on your second question: all you have to do is to Convert to 1.

0.39789711297139907/(Meter^3*(Kilogram/(Joule*Second^2))^(3/2));
Convert[%, 1]
0.397897

Needs["Miscellaneous`V4ExtendUnits`"]
Needs["Miscellaneous`V4ReducedUnits`"]
Needs["Miscellaneous`PhysicalConstants`"]

0.39789711297139907/(Meter^3*(Kilogram/(Joule*Second^2))^(3/2)) // ToUnit[1]
0.397897

To install and use Hartree as a unit...

InstallNewUnit[Hartree -> 27.211 ElectronVolt]

50 Erg // ToUnit[Hartree]
1.14687*^12*Hartree

20Hartree // ToUnit[Rydberg]
39.9989 Rydberg

To install atomic units...

e = ElectronCharge;
me = ElectronMass;
\[HBar] = PlanckConstantReduced;

SetupReducedUnits[{\[HBar], a0, me, e}, {Kelvin}]
{Ampere -> 150.97490094886209,
Kilogram -> 1.0977693252662292*^30,
Meter -> 1.889726133921251*^10,
Second -> 4.134137333612569*^16}

SpeedOfLight // ReducedUnits
137.036

En == (1/2)*(\[HBar]^2/(me*a0^2))*(Z^2/n^2)//ReducedUnits
En == 0.5*Z^2/n^2

50Erg // ReducedUnits
ReducedEquivalent[%, 1, Meter]
1.146856*^12
60.689 Meter

David Park

From: Curt Fischer [mailto:crf3 at po.cwru.edu]
To: mathgroup at smc.vnet.net

On a sort-of related note, does anyone know when quantum chemistry units
(energy in Hartrees, distance is Bohrs, etc) will find there way into the
Miscellaneous`Units` package?

Also, is there any good way to get Mathematica to simplify expressions such
as
0.39789711297139907/(Meter^3*(Kilogram/(Joule*Second^2))^(3/2))?  Plain
inspection shows that the units all cancel out, but the Miscellaneous`Units`
package doesn't do the job.  In general, the problem seems to be with units
to some non-integer power.

--
Curt Fischer

```

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