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Let (p, q) and (P, Q) be two pairs of canonical variables. The transformation Q = qα cos(βp), P = qα sin(βp) is canonical for
  • a)
    α = 2, β = 1/2
  • b)
    α = 2, β = 2
  • c)
    α = 1, β = 1
  • d)
    α = 1/2, β = 2
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Let (p, q) and (P, Q) be two pairs of canonical variables. The transfo...
This transformation is a simple substitution where the variable Q is equal to the variable q. In other words, Q and q are the same variable, just represented by different symbols.
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Community Answer
Let (p, q) and (P, Q) be two pairs of canonical variables. The transfo...
For canonical transformation we have:

⇒ αqα−1 cos(βp) × qα β cos(βp) − qα β(−sin(βp)) × αqα−1 sin(βp) = 1
αq2α−1 β(cos2 βp + sin2 βp) = 1 ⇒ αβq2α−1 = 1 ⇒ α = 1/2, β = 2.
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Let (p, q) and (P, Q) be two pairs of canonical variables. The transformation Q = qαcos(βp), P = qαsin(βp) is canonical fora)α = 2, β = 1/2b)α = 2, β = 2c)α = 1, β = 1d)α = 1/2, β = 2Correct answer is option 'D'. Can you explain this answer?
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Let (p, q) and (P, Q) be two pairs of canonical variables. The transformation Q = qαcos(βp), P = qαsin(βp) is canonical fora)α = 2, β = 1/2b)α = 2, β = 2c)α = 1, β = 1d)α = 1/2, β = 2Correct answer is option 'D'. Can you explain this answer? for UGC NET 2024 is part of UGC NET preparation. The Question and answers have been prepared according to the UGC NET exam syllabus. Information about Let (p, q) and (P, Q) be two pairs of canonical variables. The transformation Q = qαcos(βp), P = qαsin(βp) is canonical fora)α = 2, β = 1/2b)α = 2, β = 2c)α = 1, β = 1d)α = 1/2, β = 2Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for UGC NET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let (p, q) and (P, Q) be two pairs of canonical variables. The transformation Q = qαcos(βp), P = qαsin(βp) is canonical fora)α = 2, β = 1/2b)α = 2, β = 2c)α = 1, β = 1d)α = 1/2, β = 2Correct answer is option 'D'. Can you explain this answer?.
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