# Units in a quantum barrier problem

ClaesF
I have a quesion regarding a quantum physics assignemnt, I wonder what units I should use when calculating the transmission coefficient of a quantum barrier problem.

I have got the following expression:

$$T = \frac{4(E+V_0)}{(2E+V_0)cos^2a\sqrt{\frac{2m}{\hbar^2}(E-V_0)} + (E-V_0+\frac{E(E+V_0)}{E-V_0}+2\sqrt{E(E+V_0)})sin^2a\sqrt{\frac{2m}{\hbar^2}(E-V_0)}}$$

where

T = the transmission coefficient
E = the energy of an incoming electron = 2.1 eV
$V_0$ = a potential = 1.5 eV
a = a point along the x-axis = 12 angstrom (= $12*10^{-10}$ m)
m = the mass of the electron (= $9.109*10^{-31}$ kg)
$\hbar$ = $1.0546*10^{-34}$ Js or $6.582*10^{-16}$ eVs.

I don't know if I should translate all values in the whole expression into SI units, or if I somehow can use the values given in the assignment in eV and angstrom directly?
If I use the eV- and angstrom values, I guess it is wrong to use the kg-value of the electronmass in the $\sqrt{\frac{2m}{\hbar^2}(E-V_0)}$-expressions.

## Answers and Replies

gnpatterson
If you use one of the planks constants in one form (Js) and one in the other form (eVs) in the h^2 expression it should work out OK.

If you think about getting the final expression inside the trig functions to be unitless. Remember J=kg m/s

ClaesF
ok, but I must still express a in meters(=$12*10^{-10}$m) then. (Js=$kgm^2/s$)

thanks for the help.

/Claes

Staff Emeritus