 Solution

ID: past-exam-of-the-theoretical-physics-i-course-of-the-university-of-cambridge/2015/paper-1/3/b/solution

For

H = p cosh (2 q)

\overset{q}{˙} = cosh (2 q), \overset{p}{˙} = - 2 p sinh (2 q) .

O = e^{qp}

are

O_{q} = p e^{qp}

and

O_{p} = q e^{qp}

H

is therefore

\dot{O} = {O, H} = p e^{qp} [cosh (2 q) - 2 q sinh (2 q)] .

\dot{O} = e^{qp} (p \overset{q}{˙} + q \overset{p}{˙})

, gives the same expression and checks the bracket sign.

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