Tru Physics

Problem 7.2 – Griffith’s Intro to QM

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Problem 7.2

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

E_n = (n+1/2) \hbar \omega \text{, } (n=0,1,2, ...),

where \omega = \sqrt{k/m} is the classical frequency. Now suppose the spring constant increases slightly: . (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 \epsilon, 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). Hint: It is not necessary—in fact, it is not permitted—to calculate a single integral in doing this problem.

Solution:

Problem 7.2 - Griffith's Intro to QM

Problem 7.2 Solution (Download)

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