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**Unformatted text preview: **3. A 1-dimensional particle has a wavefunction: ψ = Axe-x 2 L 2 (1) Normalize the wavefunction. That is, for a given value of L , ﬁnd A such that: Z ∞-∞ ψ 2 dx = 1 (2) What are the units of L and A ? 4. Consider a hydrogen atom in its ground state. If the uncertainty in the electron’s position equals the Bohr radius, then what is the uncertainty in the electron’s momentum? What is the mean value of the momentum that you derive from the kinetic energy of the electron? How does this mean value compare with the uncertainty derived in the previous part of this problem? 5. Assume a very simple model of a diatomic molecule with two atoms of mass m 1 and m 2 separated by a distance d . What is the moment of inertia of this molecule? If the angular momentum is quantized in units of ~ what are the energy levels? 1...

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