- #1

Mechdude

- 117

- 1

## Homework Statement

first this is indeed a class assignment , but for some reason i can not remember how to do it since its a review fro a previous semesters course.

here it is

Consider a diatomic molecule with a toms labelled A and B and witha classical Hamilitonian given by

[tex] H =\frac{1}{2} M_A (\dot{x}^2_A + \dot{y}^2_A + \dot{z}^2_A ) + \frac{1}{2} M_B (\dot{x}^{2}_{B} + \dot{y}^{2}_{B} + \dot{z}^{2}_{B}) + V(\vec{r})

[/tex]

where [itex] r = \left[ (x_A - x_B)^2 + (y_A-y_B)^2 + (z_A-z_B)^2 \right]^\frac{1}{2} [/itex] is the distance between the atoms and [itex] \vec{r_A} = (x_A,y_B,z_B) [/itex] and [itex] \vec{r_B} = (x_B,,y_B,z_B) [/itex] are vectors that locate each atom.

a ) Show using the variable [itex] R= (X,Y,Z) [/itex] and [itex] \vec{r} = (x,y,z) [/itex] defined by [itex] R = \frac{(m_A \vec{r_A} + m_B \vec{r_B})}{m_A + m_B} [/itex] and [itex] \vec{r} = \vec{r_A} - \vec{r_B} [/itex] that

[tex] H = \frac{1}{2}M (\dot{X}^2 + \dot{Y}^2 + \dot{Z}^2 ) + \frac{1}{2} \mu (\dot{x}^2 +\dot{y}^2 + \dot{z}^2 ) + V(\vec{r})

[/tex]

where [itex] M =m_A + m_B [/itex] and [itex] \frac{m_A m_B}{ m_A + m_B } [/itex]

## Homework Equations

Newtons laws

## The Attempt at a Solution

i really need a clue to get started

but i think my problem is getting the total energy in c.o.m. coordinates, i can not figure out where the second term in the c.o.m. hamilitonian comes from.