(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A beam of electrons of KE = 100 eV is incident from the left on a barrier

which is 200 eV high and 10 nm wide. If the momentum spread is sufficiently

narrow, then a simple plane wave is a good approximation. Recall that the mass of an

electron is mc2 = 511 keV.

.................._____

.........1.......|..2...|............3

__________|.......|____________

..............x=0....x=10 nm

(periods are there to preserve picture upon post)

If the energy of the electrons is raised to 350 eV, what thickness should the barrier be

to give transmission with no reflections?

2. Relevant equations

[tex]T=|t|^2= \frac{1}{1+\frac{V_0^2\sin^2(k_1 a)}{4E(E-V_0)}}[/tex]

where [tex]k_1=\sqrt{2m (V_0-E)/\hbar^{2}}[/tex]

3. The attempt at a solution

I am almost positive I just use the above equation, set [tex]T=1[/tex], then solve for [tex]a[/tex] because we know every other variable. I ended up with the general equation (no substitution for values yet)

[tex]1=\frac{1}{1+\frac{V_0^2\sin^2(k_1 a)}{4E(E-V_0)}}\iff 1=1+\frac{V_0^2\sin^2(k_1 a)}{4E(E-V_0)}\iff 0=\frac{V_0^2\sin^2(k_1 a)}{4E(E-V_0)}\iff 0=\sin^2(k_1 a)\iff n\pi=\sqrt{2m (V_0-E)/\hbar^{2}}a[/tex]

[tex]\iff a=\frac{n\pi}{\sqrt{2m (V_0-E)/\hbar^{2}}}[/tex].

This solution makes me uneasy for some reason. Can someone point me out if I am wrong?

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# Total Transmission Across Finite Barrier Potential with E>V

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