Units in quantum mechanical problem about 4-He

  • #1

Homework Statement


Units of the problem are chosen to be such as KB = 1 and ħ = 1 so that energies are expressed in Kelvin and lengths in Å. The professor says the resulting value of ħ2 / 2 m for a 4-He atom is 6.0599278: how is that possibile?

Homework Equations


Natural units websites give many conversion factors:
https://thespectrumofriemannium.wordpress.com/2013/01/30/log070-natural-units/
http://en.wikipedia.org/wiki/Natural_units

The Attempt at a Solution


as the 4-He mass is
m ≈ 6 * 10-27 Kg
ħ2 / 2 m ≈ 8,4 * 10^-43 m2/s
Now using conversions of meters and seconds to eV (given at https://thespectrumofriemannium.wordpress.com/2013/01/30/log070-natural-units/) we find
m2/s ≈ 0,0169
so the result is wrong.

I tried in many other ways, starting for example from ħ = 1 and converting the 4-He mass, but I cannot find any way to get the result
ħ2 / 2 m ≈ 6.0599278

Thank you very much in advance for your help!
 

Answers and Replies

  • #2
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Edit: Found it
Just multiply and divide by constants until the units are right.
 
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  • #3
DrClaude
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Units of the problem are chosen to be such as KB = 1 and ħ = 1 so that energies are expressed in Kelvin and lengths in Å.
That's not sufficient to define a set of units. kB = 1 only sets the temperature scale, and [ħ] = [M][L]2[T]-1, so you can still set any two out of mass, length, and time. If you take Å as the unit of lenght, that leaves mass or time.

By the way, setting kB = 1 is usually used the other way around: it allows to express temperature using units of energy.

The professor says the resulting value of ħ2 / 2 m for a 4-He atom is 6.0599278: how is that possibile?
By setting the units of mass as ##\approx 8.055 \times 20^{-26}\ \mathrm{kg}##, which is a bit weird. Maybe time is set by some other constant?

 
  • #4
Thank you very much for your replies!
So it seems like the information ħ = 1 is actually not needed at all: if I get it right, we just use KB = 1 to use K instead of J and then use Å instead of m. Right? :)
Thank you again! ^ ^
 

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