Does there exists a common eigenbasis of the energy operator $T=p^2/2m$ and the momentum operator $p=-i\hbar\, d/dx$ for a particle in a 1-dimensional box of length $L$?
Thanks in advance.
Asked
Active
Viewed 123 times
1
-
The answer of if they exist lie in computing the commutator $[p^2, p]$, if it is zero then you can create such a basis – Triatticus Oct 17 '16 at 14:27
-
The commutator is zero. However, the eigenstates of T must be zero at the boundary of the box and the eigenstates of the momentum operatore can not vanish at the boundary! – Oct 17 '16 at 15:58