Chapter 7, Problem 7.34P

(a)

To determine

The Eigen states of ${\widehat{H}}_0$.

1. (i) Show that any Eigen state ${\psi }_0^1$ is same as ${\widehat{H}}_0$.
2. (ii) Show that the good states ${\psi }^0=\alpha {\psi }_a^0+{\psi }_b^0$ is determines by Equation 7.30 are Eigen states of ${\widehat{H}}_0$ with energies $E^0+E_{+}^{|}$.

(b)

To determine

The expression for the energy to second order for the states.