# Tagged Questions

I'm having trouble understanding the step $$\left[\pi (\vec{x},t),\int d^{3}y ~(\frac{1}{2} \pi (\vec{y},t)^{2}+\frac{1}{2}\phi (\vec{y},t)(-\nabla^{2} +m^{2})\phi (\vec{y},t)) \right]$$ $$=\int ... 1answer 162 views ### Finding the creation/annihilation operators Using Minkowski signature (+,-,-,-), for the Lagrangian density$${\cal L}=\partial_{\mu}\phi\partial^{\mu}\phi^{\dagger}-m^2\phi \phi^{\dagger}$$of the complex scalar field, we have the field ... 1answer 113 views ### Why don't we use Hamilton-Jacobi method in QM? In classical mechanics, we usually try to find a set of coordinates by Hamilton-Jacobi method to transform the Hamiltonian to zero such that the coordinates are conservations. However, we never try ... 3answers 288 views ### EQUAL TIME commutation relations Why is equal time commutation relation used in canonical quantization of free fields? 2answers 335 views ### Canonical equal time commutation relations in QED I understand that to quantize the classical electromagnetic field one needs to impose commutation relations and express the field in terms of creation and annihilation operators. I notice that the ... 1answer 411 views ### Quantum mechanical analogue of conjugate momentum In classical mechanics, we define the concept of canonical momentum conjugate to a given generalised position coordinate. This quantity is the partial derivative of the Lagrangian of the system, with ... 1answer 353 views ### Canonical transformation and Hamilton's equations I was trying to prove, that for a transformation to be Canonical, one must have a relationship:$$ \left\{ Q_a,P_i \right\} = \delta_{ai} $$Where Q_a = Q_a(p_i,q_i) and P_a = P_a(p_i,q_i). Now ... 3answers 440 views ### Generalizing Heisenberg Uncertainty Priniciple Writing the relationship between canonical momenta \pi _i and canonical coordinates x_i$$\pi _i =\text{ }\frac{\partial \mathcal{L}}{\partial \left(\frac{\partial x_i}{\partial t}\right)} ...
Is there any significance to: $\langle[H,\hat{O}]\rangle =0$ (which can easily be shown) where $H$ is the Hamiltonian, $\hat{O}$ is an arbitrary operator? Thanks.