Potential operator in positional space

1. Sep 20, 2004

qubits

Is the potential operator (in positional/space basis) of the Hamiltonian always diagonal in that basis? And is the kinetic energy operator always diagonal in complementary momentum space?

2. Sep 21, 2004

Eye_in_the_Sky

For a spinless particle in one dimension, the most general Hamiltonian which satisfies Galilean invariance is

Ht = P2/2m + Vt(Q) .