The eigenfunctions of the Hamiltonian $\mathrm{H}(\mathrm{H}=\mathrm{T}+\mathrm{V})$ of a harmonic oscillator are (where T and V are kinetic energy and potential energy operators, respectively)
(a)eigenfunctions of T as well as V
(b)eigenfunctions of T, but not of V
(c)eigenfunctions of V, but not of T
(d)eigenfunctions of neither T nor V
Answer
Answer: D ✓ checked by 4AB · confidence high
Explanation
T and V do not commute with each other or with H (x and p do not commute), so the oscillator eigenfunctions are eigenfunctions of neither T nor V separately.