Question

Consider the Hamiltonian H = p1^2 / 2m + 1 / 2m (p - kq1)^2 Determine the constants A and B so that the transformation Q1 = Ap1, P1 = p2 - kq1, Q2 = B(p1 - kq2), P2 = p2, is canonical. Use this canonical transformation to solve the equations of motion of the transformed Hamiltonian, find q1(t), q2(t), p1(t) and p2(t).

          Consider the Hamiltonian

H = p1^2 / 2m + 1 / 2m (p - kq1)^2

Determine the constants A and B so that the transformation

Q1 = Ap1, P1 = p2 - kq1, Q2 = B(p1 - kq2), P2 = p2,

is canonical.

Use this canonical transformation to solve the equations of motion of the transformed Hamiltonian, find q1(t), q2(t), p1(t) and p2(t).

Consider the Hamiltonian

H = p1^2 / 2m + 1 / 2m (p - kq1)^2

Determine the constants A and B so that the transformation

Q1 = Ap1, P1 = p2 - kq1, Q2 = B(p1 - kq2), P2 = p2,

is canonical.

Use this canonical transformation to solve the equations of motion of the transformed Hamiltonian, find q1(t), q2(t), p1(t) and p2(t).

Added by Lindsay W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sri K

06/16/2022

Step 1

This means that the Poisson brackets of the new variables must satisfy the canonical Poisson bracket relations: {Q1, P} = 1 {Q2, Pz} = 1 Let's calculate these Poisson brackets: {Q1, P} = {Ap1, P} = A{p1, P} = A {Q2, Pz} = {B(p1 + kq2), p2} = B{p1 + kq2, p2} = Show more…

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Consider the Hamiltonian H = p1^2 / 2m + 1/2m (p - kq1)^2 Determine the constants A and B so that the transformation Q1 = Ap1, P1 = p2 - kq1, Q2 = B(p1 - kq2), P2 = p2, is canonical. Use this canonical transformation to solve the equations of motion of the transformed Hamiltonian, find q1(t), q2(t), p1(t) and p2(t).