Write the Lagrangian for the case V11 = V22 = 0 and V12 = V21 > 0 for the example discussedin Eqs. (6.27) to (6.30). Show there is one normal mode of simple harmonic motion with the frequency ω1 = (V12)1/2, and a second mode in which the particle is unbound, receding exponentially to infinity for long time t > τ in accordance with the expression e−t/τ, where the parameter τ is given by τ = (V12)−1/2. For this unbounded mode, how does the distance depend upon time when t<τ? What is the nature of the point x1 = x2 = 0? Restate your results with the mass parameter m included explicitly.
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