Word Count : 372

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To show that the given transformation is canonical, we use the symplectic condition for a canonical transformation. The transformation is given as: \[ Q = \log(1+\sqrt{q}\cos p) \] \[ P = 2(1+\sqrt{q}\cos p)\sqrt{q}\sin p \] ### Step 1: Compute the Jacobian Matrix For a transformation \((q, p) \to (Q, P)\), the Jacobian matrix is given by: \[ J = \begin{bmatrix} \frac{\partial Q}{\partial q} & \frac{\partial Q}{\partial p} \\ \frac{\partial P}{\partial q} & \frac{\partial P}{\partial p} \end{bmatrix} \] We compute the partial derivatives of \( Q \) and \( P \): #### Partial Derivatives ___ __________ __________ __________ ____ ________ _______ ____.
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