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Units in quantum mechanical problem about 4-He

  1. Jan 15, 2015 #1
    1. The problem statement, all variables and given/known data
    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?

    2. Relevant 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

    3. 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!
     
  2. jcsd
  3. Jan 15, 2015 #2

    mfb

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    2016 Award

    Staff: Mentor

    Edit: Found it
    Just multiply and divide by constants until the units are right.
     
    Last edited: Jan 15, 2015
  4. Jan 15, 2015 #3

    DrClaude

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    Staff: Mentor

    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.

    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?

     
  5. Jan 16, 2015 #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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