# Tagged Questions

304 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 ...
338 views

### Heisenberg picture of QM as a result of Hamilton formalism

Let's have formula of full time-derivative of physical value in Poisson's formalism: $$\tag{1} \frac{df}{dt} = -[H, f]_{P. br.} + \frac{\partial f}{\partial t},$$ where $[A, B]_{P. br.}$ is Poisson's ...
316 views

### Full time-derivative of a function and Schrodinger equation

From Hamiltonian formalism there is well known equation, $$\frac{d F}{dt} = \frac{\partial F}{\partial t} + \{F, H\}_{PB},$$ where $\{H, F\}_{PB}$ is the Poisson bracket. After using Hamiltonian ...
185 views

### The correspondence between Poisson bracket and Commutators in Quantum Mechanics

I don't understand canonical quantization. In passing from classical to quantum, one replaces the Poisson brackets with the commutators. I don't really understand this. How can we generally show that ...
330 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 ...
In Dirac's book Principles of quantum mechanics (4th ed., pgs 87-88), he seems to give a very elementary argument as to how the commutator $[X,P]$ reduces to the Poisson brackets ${x,p}$ in the limit ...
The Poisson bracket is defined as: \{f,g\}_{PB} ~:=~ \sum_{i=1}^{N} \left[ \frac{\partial f}{\partial q_{i}} \frac{\partial g}{\partial p_{i}} - \frac{\partial f}{\partial p_{i}} \frac{\partial ...