513.001 Molecular and Solid State Physics | |
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Approximate wavefunctionOften in molecular or solid state physics we know the Hamiltonian but we can't solve the Schrödinger equation associated with this Hamiltonian. In these cases we often guess a solution and then calculate the corresponding energy. Consider the Hamiltonian for a hydrogen atom. In spherical coordinates it is, Find the expectation value of the energy, for the wavefunction Note that this wavefunction is not an eigenfunction of the Hamiltonian. Here a0 = 5.3 × 10-11 m is the Bohr radius. (You may use a computer algebra program to solve this problem.) |