Homework Statement
Consider a canonical transformation with generating function
F_2 (q,P) = qP + \epsilon G_2 (q,P),
where \epsilon is a small parameter.
Write down the explicit form of the transformation. Neglecting terms of order \epsilon^2 and higher,find a relation between this...
Homework Statement
Show directly that the transformation; Q=log(1/q*sinp), P=q*cotp is canonical.Homework Equations
Since these equations have no time dependence, the equations are canonical if (with d denoting a partial derivative)
dQ_i/dq_j = dp_j/dP_i, and dQ_i/dp_j = -dq_j/dP_i
The...
Hi, I tried to solve this problem, but I was unsuccessful
Here is the problem:
Given the transformation:
\left \{ \begin{array}{l} Q = p^\gamma \cos(\beta q) \\ P = p^\alpha \sin(\beta q) \end{array} \right.
a) Determine the values of the constants \alpha , \beta and \gamma...
Hello,
I need to solve the Hamiltonian of a one-dimensional system:
H(p, q) = p^2 + 3pq + q^2
And I've been instructed to do so using a canonical transformation of the form:
p = P \cos{\theta} + Q \sin{\theta}
q = -P \sin{\theta} + Q \cos{\theta}
And choosing the correct angle so...
Problem: Verify that the infinitesimal transformation generated by any dynamical variable g is a canonical transformation.
I've worked out that an infinitesimal canonical transformation can be represented as follows:
q_i -> q_i' = q_i + ε(∂g/∂p_i) ≡q_i + δq_i...
Canonical Transformation and renormalization...
Let be L a lagrangian of a Non-Renormalizable theory..then we could take its hamiltonian.
Then after taking Hamiltonian you could take a Canonical Transformation to find another (renormalizable) Hamiltonian..and solve it..¿why this trick is...