For the harmonic oscillator [V(x) = (1/2)kx 2 ], the allowed energies are where = k/m

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For the harmonic oscillator [V(x) = (1/2)kx2], the allowed energies are

where ω = √k/m is the classical frequency. Now suppose the spring constant increases slightly: k→ (1+∈)k. (Perhaps we cool the spring, so it becomes less flexible.)
(a) Find the exact new energies (trivial, in this case). Expand your formula as a power series in ϵ, up to second order.
(b) Now calculate the first-order perturbation in the energy, using Equation 7.9. What is H' here? Compare your result with part (a).

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Introduction To Quantum Mechanics

ISBN: 9781107189638

3rd Edition

Authors: David J. Griffiths, Darrell F. Schroeter

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