Understanding Atomic Units for Beginner Mathematicians

[brydustin]

Hi, I know nearly nothing about physics, I'm a mathematician working on a computer program.
Anyway, I have to write a program and my boss suggested that I use atomic units and that at the end of the program I can "scale up" to natural units if desired. I tried to read up on these units, but they intuitively make no sense they just seem artificial and I don't know how to handle it. For example, what are the atomic units for:
h_bar, length, time, temperature, and energy.
And do they really have "units" attached or are the unitless numbers -- I read somewhere that physicists do this to also blur the lines between time and lenght... all seems strange to me, any help, please!

 

[Drakkith]

Why can't you just use the standard units for all that? Meter, kelvin, joule, ETC.

 

[brydustin]

Why can't you just use the standard units for all that? Meter, kelvin, joule, ETC.

Yeah, that's what I thought too. Apparently, my boss just wants me to use atomic units.

 

[Drakkith]

Yeah, that's what I thought too. Apparently, my boss just wants me to use atomic units.

Hrmm. Have you asked him why he wants you to do this? Would it somehow be easier in the long run?

 

[qsa]

http://en.wikipedia.org/wiki/Natural_units

 

[brydustin]

http://en.wikipedia.org/wiki/Natural_units

Well, for example, how would you define a Kelvin temperature in atomic units?
For example, what would the room temperature be in atomic units. Of course, I've already seen this wikipedia article; but it means nothing to me.

To say that temperature is defined as:

T_A = {m_e e^4} / {\hbar^2 (4 \pi \epsilon_0)^2 k_B}

means a lot of nothing to me,because I don't see how the temperature can change if all the values in the equation are 1 anyway.

 

[marcus]

...

To say that temperature is defined as:

T_A = {m_e e^4} / {\hbar^2 (4 \pi \epsilon_0)^2 k_B}

means a lot of nothing to me,because I don't see how the temperature can change if all the values in the equation are 1 anyway.

That's how the temperature UNIT is defined in (Hartree) atomic units. So it is not supposed to change.

Hopefully someone else will jump in who is more used to Atomic Units. (I am more familiar with Planck Units). But in case no one immediately offers to help you, I will suggest that you can make it mean something to you, if you try. In all these systems of nature-based units the unit of temperature is simply equal to the unit of energy divided by the Boltzmann k_B

So if you want to know in METRIC what is the atomicunit of energy, take what they say for the temp unit (in wikiped they give a Kelvin value) and multiply the metric value for the temp unit times the metric value of k_B.


You could also look at what you wrote for the atomicunit of temperature, and multiply it by k_B and that will give the atomicunit of energy, E_A

E_A = {m_e e^4} / {\hbar^2 (4 \pi \epsilon_0)^2 }

Now I guess you could look at that and try to make sense of it as a unit of energy.

It looks to me like it might be the electron mass multiplied by the speed of light squared or some such thing.

 

[qsa]

Well, for example, how would you define a Kelvin temperature in atomic units?
For example, what would the room temperature be in atomic units. Of course, I've already seen this wikipedia article; but it means nothing to me.

To say that temperature is defined as:

T_A = {m_e e^4} / {\hbar^2 (4 \pi \epsilon_0)^2 k_B}

means a lot of nothing to me,because I don't see how the temperature can change if all the values in the equation are 1 anyway.

from the table in the link, kelvin =1/3.1577e5 atomic unit of temp