Units in quantum mechanical problem about 4-He

[physicsisgreat]

Homework Statement

Units of the problem are chosen to be such as K_B = 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!

 

[mfb]

Edit: Found it
Just multiply and divide by constants until the units are right.

 

[DrClaude]

Units of the problem are chosen to be such as K_B = 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. k_B = 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 k_B = 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?

 

[physicsisgreat]

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 K_B = 1 to use K instead of J and then use Å instead of m. Right? :)
Thank you again! ^ ^