The transformation Q = λq, p = λP is canonical while the same transformation with t time dilatation, Q = λq, p = λP, t' = λ2t, is not. Show that the equations of motion for q and p for the Hamiltonian H = p2/2 − 1 / (2 q2) are invariant under this transformation.
The transformation Q = λq, p = λP is canonical while the same transformation with t time dilatation, Q = λq, p = λP, t' = λ2t, is not. Show that the equations of motion for q and p for the Hamiltonian H = p2/2 − 1 / (2 q2) are invariant under this transformation.
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Question
The transformation Q = λq, p = λP is canonical while the same
transformation with t time dilatation, Q = λq, p = λP, t' = λ2t, is not. Show
that the equations of motion for q and p for the Hamiltonian
H = p2/2 − 1 / (2 q2)
are invariant under this transformation.
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