Units in a quantum barrier problem

In summary, the transmission coefficient (T) for a quantum barrier problem can be calculated using the 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 E is the energy of an incoming electron, V_0 is the potential, a is a point along the x-axis, m is
  • #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.
 
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  • #2
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
 
  • #3
ok, but I must still express a in meters(=[itex]12*10^{-10}[/itex]m) then. (Js=[itex]kgm^2/s[/itex])

thanks for the help.

/Claes
 
  • #4
You want the argument in the trig terms to be unitless. Write "a" in meters and the terms inside the square roots in SI units (so the units of the wave vector will be 1/meter).

You can leave the energies outside the trig terms in eV or SI, since the transmission coefficient is the ratio of these energy terms.
 

1. What is a quantum barrier problem?

A quantum barrier problem refers to a scenario in quantum mechanics where a particle encounters a potential barrier, such as a wall or barrier, that it does not have enough energy to pass through. This results in the particle behaving like a wave and exhibiting phenomena such as tunneling and reflection.

2. What are the units used in a quantum barrier problem?

The units used in a quantum barrier problem depend on the specific problem and the system being studied. However, some commonly used units include length (e.g. nanometers), energy (e.g. electron volts), and time (e.g. femtoseconds).

3. How is the barrier height and width measured in a quantum barrier problem?

The barrier height is typically measured in energy units (e.g. electron volts) and represents the energy required for a particle to pass through the barrier. The barrier width is measured in length units (e.g. nanometers) and represents the physical distance of the barrier.

4. What is the role of units in solving a quantum barrier problem?

Units are crucial in solving a quantum barrier problem as they provide a way to quantify the physical properties and parameters of the system being studied. They also help in converting between different systems of measurement and in ensuring the accuracy and consistency of calculations.

5. How do units affect the behavior of particles in a quantum barrier problem?

The specific units used in a quantum barrier problem can affect the behavior of particles in different ways. For example, changing the energy unit can change the barrier height and thus impact the likelihood of tunneling. Similarly, changing the length unit can affect the barrier width and the probability of reflection. Therefore, the choice of units can significantly impact the results of a quantum barrier problem.

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