A 1500 kg car moving at approaches a hill that is 24 m high and 30 m long. We have to find the probability that the car will tunnel quantum mechanically through the hill, appearing on the other side. That is we have to find the car’s transmission coefficient for this hill.

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The quantum transmission probability for a particle of mass m, kinetic energy E for tunnelling through a potential barrier of height U and width L is approximately given by the following function

Mass of the car, ,

speed of the car, ,

kinetic energy of the car, ,

height of the hill, .

Therefore, the gravitational potential energy of the car in order to cross the hill will be, .

The width of the hill, .

Therefore, the quantum transmission probability for the car to tunnel through the will be approximately given by the function

And