(a) Compute ‹x›, ‹p› ‹x2› and ‹p2›, for the states ψ0 (Equation 2.59) and ψ1 (Equation 2.6...

(a) Compute ‹x›, ‹p› ‹x2› and ‹p2›, for the states ψ0 (Equation 2.59) and ψ1 (Equation 2.62), by explicit integration. Comment: In this and other problems involving the harmonic oscillator it simplifies matters if you introduce the variable  and the constant.

(b) Check the uncertainty principle for these states.

(c) Compute ‹T› (the average kinetic energy) and ‹V› (the average potential energy) for these states. (No new integration allowed!) Is their sum what you would expect?