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Unformatted text preview: Problem Set 08 Note: This problem set is due Nov 08 before midnight. Please leave it in my mailbox located at the first floor of Rutherford building. 1. Consider a two dimensional Hilbert space with basis vectors | φ 1 i and | φ 2 i that are eigenstates of an unperturbed Hamiltonian H . Let us assume that the system is perturbed by a time dependent perturbation W such that the perturbed Hamiltonian H 1 = H + W is defined as H 1 = H 11 H 12 H 21 H 22 (1) where H ij are all functions of time. Imagine now that we have another identical copy of the system which is perturbed by a time independent Hamiltonian H 2 = h 11 h 12 h 21 h 22 (2) with h ij being time independent. Clearly, if we start with an initial state | ψ (0) i , then this state will evolve to either | ψ 1 ( t ) i or | ψ 2 ( t ) i depending on whether the perturbation is done by the Hamiltonian H 1 or H 2 respectively. We also expect in general | ψ 1 ( t ) i 6 = | ψ 2 ( t ) i ....
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- Fall '05
- mechanics, hydrogen atoms, nitrogen atom, Time dependent perturbation, unperturbed Hamiltonian H0, perturbed Hamiltonian H1