Recent content by Loxias

Ok, this is what I did : Q = 2ia(P + 2q) , P = \frac{p-iaq}{2ia} which means that Q and p are independent coordintes, which means the generating function will be of the third kind, F_3(Q,p) . for the third kind, q = -\frac{\partial F_3}{\partial p} = \frac{p}{ia}-2P P = -\frac{\partial...

Homework Statement Given the transformation Q = p+iaq, P = \frac{p-iaq}{2ia} Homework Equations find the generating function The Attempt at a Solution As far as I know, one needs to find two independent variables and try to solve. I couldn't find such to variables. I've...

Good luck on your exam!

If I remember correctly, the half in the quantum hamiltonian is the vacuum energy, and is a quantum effect, not classical. (This all may be wrong, don't take me up for it :) )

I think you are treating a, a* as operators (used commuting relation in the last part, if I'm not mistaken), while here they are simply coordinates, and aa* = a*a. Please note that you expressed p^2, q^2 in a wrong way but then corrected it in H. Also, my algebra is waa^* = \frac{mw^2}{2}...

I rechecked part a again, and also solved it using another method, got the same answer. I also think It's right since it resembles the quantum hamiltonian, without \hbar and \frac{1}{2} , which makes sense. For the third part, I used \dot{a} = \{a,h\} and solved it. Before I did that...

Thanks :smile:

Homework Statement The Hamiltonian for the one-dimensional harmonic oscillator is given by: H = \frac{p^2}{2m}+ \frac{mw^2q^2}{2} Homework Equations (a) Express H in terms of the following coordinates: a = \sqrt{\frac{mw}{2}} (q+i\frac{p}{mw}) a^* = \sqrt{\frac{mw}{2}} (q-i\frac{p}{mw})...

Thank you for clarifying this. Could you elaborate more about what you meant with the legendere transform?

Homework Statement The mechanics of a system are described by the Lagrangian: L = \frac{1}{2}\dot{x}^2 + \dot{x}t Homework Equations (a) Write the Energy (Jacobi function) for the system. (b) Show that \frac{dh}{dt} \neq \frac{\partial h}{\partial t} (c) Write an expression for...

thanks :smile:

indeed.. i saw where i went wrong. thanks alot! so the hamiltonian here is the energy of the system?

I'm trying to see what i did wrong and i can't find it. Can you see it?

T = \frac{m}{2} (\dot{x}^2 + \dot{y}^2 + \dot{z}^2) and according to my first post, you can see where all the terms came from. also, \dot{R} = 0 a small mistake, the last term should be \dot{\theta}^2R^2sin^2(\theta)

the Lagrangian is L = \frac{m}{2} \left(\dot{\theta}^2R^2 + w^2R^2sin^2(\theta) + \dot{\theta}R^2sin^2(\theta)\right) - mgRcos(\theta) from which I've derived the hamiltonian according to H = \frac{\partial L}{\partial \dot{\theta}}\dot{\theta} - L which is what i wrote below...