Question

A harmonic oscillator with the usual PE of V(x)= (.5)kx^2 perturbed by a small change to the spring constant k -->(1+E)k, with E<<1.

1. Write the new energy eigenvalues, making sure any parameters are clearly defined.

2. Expand the eigenvalue expression in a power series in E up to the second order using a Taylor series expansion.

3. What is the perturbation Hamiltonian in the problem?

Answer 1