Find the matrix elements and in the (orthonormal) basis of stationary states for the harmonic oscillator (Equation 2.68). You already calculated the “diagonal” elements (n = n') in Problem 2.12; use the same technique for the general case. Construct the corresponding (infinite) matrices, X and P. Show that

is diagonal, in this basis. Are its diagonal elements what you would expect? Partial

(Equation 2.68)

Problem 2.12

Find (x), (p), (x²), (p²) and (T), for the nth stationary state of the harmonic oscillator, using the method of Example 2.5. Check that the uncertainty principle is satisfied.

Transcribed Image Text:

(1/2m) p2 + (mw²/2)X² = H