Principles of Quantum Mechanics · Problem 2.5.4

Review of Classical Mechanics — R. Shankar

Physics — Quantum Mechanics · hamiltonian-two-body-problem

Problem

Show that

\mathscr{H}

corresponding to

\mathscr{L}

in Eq. (2.3.6) is

\mathscr{H} = |\mathbf{p}_{\text{CM}}|^2/2M + |\mathbf{p}|^2/2\mu + V(\mathbf{r})

, where

M

is the total mass,

\mu

is the reduced mass,

\mathbf{p}_{\text{CM}}

and

\mathbf{p}

are the momenta conjugate to

\mathbf{r}_{\text{CM}}

and

\mathbf{r}

, respectively.