Homework 3 - eigenstate is | E 1 i = A(2 | ± 1 i-i | ± 2...

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Physics 411 HW#3 Due at the start of class Wednesday, Sept 30th Reading: Class notes, Chapter 2 section 2.1 and Chapter 3 sections 3.1-3.4 in Griffiths Office Hours: Mondays, 5:00-6:30 PM in DRL 4E19 Problem 1 Consider the Hamiltonian of a spin-1 / 2 particle from the last HW: z [ ˆ H ] z = E 0 z 0 ( 3 + i ) / 2 ( 3 - i ) / 2 0 z , Suppose this Hamiltonian arises from the spin interaction ˆ H = - γ ˆ ~ S · ~ B . Find the magnitude and direction of the magnetic field ~ B . Express the magnitude in terms of E 0 , γ and ~ . Problem 2 The Hilbert space of a system is spanned by an orthonormal basis {| 1
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Unformatted text preview: eigenstate is | E 1 i = A (2 | ± 1 i -i | ± 2 i ) and it has an energy eigenvalue of Δ. The other eigenstate | E 2 i has an energy eigenvalue of-Δ. (1a) Find the normalization constant A, assuming it is real. (1b) Find | E 2 i in the {| ± i i} basis. To remove arbitrariness in the overall phase, choose the coefficient of | ± 1 i to be real. (1c) Suppose that at t = 0 the system is in the state | ± 2 i . What is the probability of being in this state for time t > 0?...
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