Crude Probability calculation for tunneling

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SUMMARY

The discussion focuses on calculating the probability of quantum tunneling for an electron encountering a potential barrier of 4 eV height and 5 x 10-11 m width. The amplitude of the wave function at the entry is given as 1, while the amplitude at the exit is calculated to be 0.00594. To determine the probability of tunneling, one must square the exit amplitude, resulting in a probability of approximately 0.0000352. The calculation method for the exit amplitude is crucial for validating the results.

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Say I have a potential barrier that is 4eV higher then an electrons energy and 5x10^-11 wide. Just by considering the change in amplitude of the wave function from the entry into the barrier vs the exit I am asked to make a rough approximation for the probability of tunnelling. I get the amplitude at entry is 1 and exit is 0.00594. Now is 0.00594 a good approximation for the probability of tunnelling or would I need to do anything else to do it.

This isn't homework it's practice for an exam which I have tomorow
 
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Recall that you need to square amplitudes to get probabilities.
 
It might also help if you tell us how you calculated the amplitude at exit so we can check your procedure.
 

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