Quantum Mech (Barriers and Tunneling)

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1. Two nanowires are separated by 1.3 nm as measured by STM. Inside the wires the potential energy is zero, but between the wires the potential energy is greater than the electron's energy by only 0.9 eV. Estimate the probability that the electron passes from one wire to the other.



2. k=sqrt(2m(V_0-E))/hbar
T=(1+V^2sinh^2(kL)/(4E(V_0-E)))^-1
T=16E/V_0(1-E/V_0)e^-2kL When kL>>1 (kL=6.31)
V_0-E=0.9 eV




3. The problem here is that I have 2 unknowns for both T equations, and I don't know if it would make sense to set them equal to each other and then solve for one of the unknowns. For either equation on its own the unknown V_0 and E do not cancel themselves out. Do I possibly need to use the equation K_min=(P)^2/(2m)=V_0-E? Or could you point me towards something I have overlooked? Would I be able to use any simple harmonic oscillator equations? Such as E_0=1/2*hbar*omega where omega^2=k/m? And then assume E_0=E? But I feel like this wouldn't make sense..
 

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