Tagged Questions
5
votes
2answers
171 views
Weyl Ordering Rule
While studying Path Integrals in Quantum Mechanics I have found that [Srednicki: Eqn. no. 6.6] the quantum Hamiltonian $\hat{H}(\hat{P},\hat{Q})$ can be given in terms of the classical Hamiltonian ...
6
votes
1answer
170 views
Operator Ordering Ambiguities
I have been told that $$[\hat x^2,\hat p^2]=2i\hbar (\hat x\hat p+\hat p\hat x)$$ illustrates operator ordering ambiguity.
What does that mean?
I tried googling but to no avail.
3
votes
2answers
154 views
Ordering Ambiguity in Quantum Hamiltonian
While dealing with General Sigma models (See e.g. Ref. 1)
$$\tag{10.67} S ~=~ \frac{1}{2}\int \! dt ~g_{ij}(X) \dot{X^i} \dot{X^j}, $$
where the Riemann metric can be expanded as,
$$\tag{10.68} ...
2
votes
1answer
145 views
Equivalence of classical and quantized equation of motion for a free field
Suppose a classical free field $\phi$ has a dynamic given in Poisson bracket form by $\partial_o\phi=\{H, \phi\}$. If we promote this field to an operator field, the dynamic after canonical ...
8
votes
2answers
299 views
Dirac equation as canonical quantization?
First of all, I'm not a physicist, I'm mathematics phd student, but I have one elementary physical question and was not able to find answer in standard textbooks.
Motivation is quite simple: let me ...
4
votes
3answers
348 views
Generalizing Heisenberg Uncertainty Priniciple
Writing the relationship between canonical momenta $\pi _i$ and canonical coordinates $x_i$
$$\pi _i =\text{ }\frac{\partial \mathcal{L}}{\partial \left(\frac{\partial x_i}{\partial t}\right)}$$
...
6
votes
2answers
291 views
How do we resolve operator ordering ambiguities when quantizing generic nonlinear second-class constraints?
Dirac came up with a general theory of constraints, including second-class constraints. To quantize such systems, he first computed the Dirac bracket classically, and only then "promoted" the ...
