Problem 3. A dynamical system is described by the Hamiltonian $H = frac{1}{2}q^2 + at^2q^2 - 2tpq + frac{1}{a}p^2$, where $a$ is a constant. Apply a canonical transformation defined by the generating function $F = frac{1}{2}atq^2 - qP$ and find the new Hamiltonian in terms of $P$ and $Q$.

          Problem 3. A dynamical system is described by the Hamiltonian
$H = frac{1}{2}q^2 + at^2q^2 - 2tpq + frac{1}{a}p^2$,
where $a$ is a constant. Apply a canonical transformation defined by the generating function
$F = frac{1}{2}atq^2 - qP$
and find the new Hamiltonian in terms of $P$ and $Q$.

$Problem 3. A dynamical system is described by the Hamiltonian H = frac12q^2 + at^2q^2 - 2tpq + frac1ap^2, where a is a constant. Apply a canonical transformation defined by the generating function F = frac12atq^2 - qP and find the new Hamiltonian in terms of P and Q.$

Added by Michelle S.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Krishna G

03/15/2022

Step 1

** Given: Generating function F = atq - qP Show more…

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Problem 3. A dynamical system is described by the Hamiltonian H = 1/2 q^2 + at^2q^2 - 2tpq + 1/a p^2 where a is a constant. Apply a canonical transformation defined by the generating function F = 1/2 atq^2 - qP and find the new Hamiltonian in terms of P and Q.