3
votes
"Constrain then quantise" vs. "quantise then constrain"
The phrase "quantization commutes with constraints" usually refers to Guillemin-Sternberg conjecture. It has only been proved for a limited class of (gauge) theories.
It should stressed that ...
- 182k
2
votes
"Constrain then quantise" vs. "quantise then constrain"
Take your first example of a particle in $\mathbb R^d$ constrained to lie on $x_1=0$. In Dirac Quantization the constraint on the wavefunctions is not $x_1 \psi(\vec x)=0$, but rather $$\frac{\partial}...
- 259
2
votes
Example of a transformation that is not canonical
One way is to spoil a canonical transformation. But in reality, canonical transformations are a very restricted subset of all possible transformations. Therefore, if you just 'randomly' pick a ...
- 123
1
vote
Accepted
Need help finding Hamiltonian for equations of motion
Hints:
The ansatz (2) is too optimistic: The generalized velocity $\dot{\theta}$ is not necessarily the canonical momentum.
Instead use the method outlined in my Phys.SE answer here to find a ...
- 182k
1
vote
Using the EoM in the canonical quantization of EM field
I think you can use the equation of motion for the simple harmonic oscillator too. The Euler Lagrange equation for the position operator $X$ is
$$\frac{d^2X}{dt^2}+\omega ^2 X=0$$
so we get:
$$X=ae^{-...
- 5,695
1
vote
Accepted
Derivation of Hamilton-Jacobi (HJ) Equation
Hamilton's principal function$^1$ $S\equiv F$ is the sole unknown variable in HJ equation. E.g. in contrast the Hamiltonian $H$ is assumed to be known.
That's how separation of variables (SOV) work. ...
- 182k
1
vote
Accepted
What are good books/chapters of books or articles to study canonical transformations in quantum mechanics at a graduate level?
I am unaware of many detailed resources in the area targeted towards typical physics graduates. However, there is a CRM monograph dealing with the Function Theory on Symplectic Manifolds which is ...
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