- #1
ClaesF
- 2
- 0
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:
[tex]
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)}}
[/tex]
where
T = the transmission coefficient
E = the energy of an incoming electron = 2.1 eV
[itex]V_0[/itex] = a potential = 1.5 eV
a = a point along the x-axis = 12 angstrom (= [itex]12*10^{-10}[/itex] m)
m = the mass of the electron (= [itex]9.109*10^{-31}[/itex] kg)
[itex]\hbar[/itex] = [itex]1.0546*10^{-34}[/itex] Js or [itex]6.582*10^{-16}[/itex] 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 [itex]\sqrt{\frac{2m}{\hbar^2}(E-V_0)}[/itex]-expressions.
I have got the following expression:
[tex]
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)}}
[/tex]
where
T = the transmission coefficient
E = the energy of an incoming electron = 2.1 eV
[itex]V_0[/itex] = a potential = 1.5 eV
a = a point along the x-axis = 12 angstrom (= [itex]12*10^{-10}[/itex] m)
m = the mass of the electron (= [itex]9.109*10^{-31}[/itex] kg)
[itex]\hbar[/itex] = [itex]1.0546*10^{-34}[/itex] Js or [itex]6.582*10^{-16}[/itex] 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 [itex]\sqrt{\frac{2m}{\hbar^2}(E-V_0)}[/itex]-expressions.