- #1
iAlexN
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Homework Statement
A particle with the energy E < V[itex]_{0}[/itex] (V[itex]_{0}[/itex] > 0) moves in the potential V(x) = 0, x<0 ; V(x)= V[itex]_{0}[/itex], 0<x<d and V(x)= 0, x>d. Measure the probability that the particle will tunnel through the barrier by calculating the absolute value of the ratio squared, |[itex]\Psi[/itex](d)/[itex]\Psi[/itex](0)|[itex]^{2}[/itex] between the values of the wave function at x=d and x = 0
Calculate the probability for an electron, when V[itex]_{0}[/itex]- E=1 eV and d = 1 Å.
Homework Equations
[itex]\Psi[/itex](x) = ae[itex]^{\kappa*x}[/itex]+be[itex]^{-\kappa*x}[/itex], [itex]\kappa[/itex] = [itex]\sqrt{2m( V_{0}-E)/\hbar^{2}}[/itex] for E<V[itex]_{0}[/itex]
The Attempt at a Solution
Firstly I get:
[itex]\kappa[/itex] = [itex]\sqrt{2m(1)/\hbar^{2}}[/itex] for E<V[itex]_{0}[/itex]
However, the problem is with this wave function:
[itex]\Psi[/itex](x) = ae[itex]^{\kappa*x}[/itex]+be[itex]^{-\kappa*x}[/itex]
In order to calculate the ratio, |[itex]\Psi[/itex](d)/[itex]\Psi[/itex](0)|[itex]^{2}[/itex], I think I have to define a and b somehow, but I don't know where to start.
Thanks!