alice in quantumland

[carmen electron]

This was one of the bonus questions on my homework. Teacher says whoever gets it right, consider yourself a god or goddess. Can anyone help me solve this?

Calculate the lowest possible energy for an electron confined in a cube of sides equal to 10pm, and a cube of sides equal to 1fm. The latter cube is about the size of a nucleus. What do your energies say about the chance of an electron being inside the nucleus? *Hint: Assuming that the uncertainty in the position of the electron is the length of a side of a cube, find the change in Energy (triangle E is symbol) for each cube.

[selfAdjoint]

From the appearance of \Delta E I assume you have been given the uncertainty principles for energy and time and for momentum and length. To use the E,t one, you have to get a \Delta t out of the box side length, and I suggest you allow your electron to have a maximum speed of c, so the time it would spend in crossing the box would be ...? And the \Delta E for that \Delta t would be...?