Question

Derive the expectation value of x^2, that is . Show that it can be expressed as (v + 1/2)h/[(2pi)√(mk)] Use the wave functions derived for the harmonic oscillator together with the Hermite polynomials and the recursion formula or other suitable methods.

b) Use the assumption that the amplitude of the vibration can be expressed as √(< ?^2 >) to calculate the amplitude (around equilibrium) of the stretching mode vibration for the hydrogen atom in the HCl molecule in its vibrational ground state. Express the amplitude both in SI units and relative to the bond length.

Answer 1