# Tagged Questions

Quantization refers to the procedure or methodology for replacing a classical system by a quantum system. If the question is about the quantized or discrete behavior of a phenomenon use the [tag:discrete] instead.

434 views

### Definition of “Quantizing”

Could anyone explain to me what "quantize" means in the following context? Quantize the 1-D harmonic oscillator for which $$H~=~{p^2\over 2m}+{1\over 2} m\omega^2 x^2.$$ I understand that the ...
1k 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.
154 views

### When can photon field amplitudes be written as field operators?

Suppose I have some classical field equation for two photon fields with amplitudes $A_1(z),A_2(z)$ (plane waves) given as ${A}_1=\alpha f(A_1,A_2) \\ {{A}_2}=\beta g(A_1,A_2)$ Under what ...
420 views

### Quantization of Nambu–Goto action in multiples of Planck's constant?

Isn't it possible? Quantization of Nambu–Goto action $$\mathcal{S} ~=~ -\frac{1}{2\pi\alpha'} \int \mathrm{d}^2 \Sigma \sqrt{{\dot{X}} ^2 - {X'}^2}~=~nh\qquad n \in\mathbb{Z}.$$
183 views

### Poincaré group on quantum Klein-Gordon field (C*-algebraic scenario)

on the same topic as this question, I have been trying to fool around with the free real K-G field in flat spacetime on the C*-algebraic scenario (Haag-Kastler axioms, Weyl quantization, etc). Since ...
748 views

### Path integral and geometric quantization

I was wondering how one obtains geometric quantization from a path integral. It's often assumed that something like this is possible, for example, when working with Chern-Simons theory, but rarely ...
1k views

### Reason for the discreteness arising in quantum mechanics?

What is the most essential reason that actually leads to the quantization. I am reading the book on quantum mechanics by Griffiths. The quanta in the infinite potential well for e.g. arise due to the ...
314 views

114 views

### understanding the oscillating part of the Gutzwiller trace

given the density of states according to Gutzwiller's trace formula $g(E)= g_{smooth}(E)+ g_{osc}(E)$ i know that the 'smooth' part comes from $g_{smooth}(E)= \iint dxdp \delta(E-p^{2}-V(x))$ ...
78 views

### shouldn't we add the oscillating terms into Bohr-Sommerfeld quantization formula

shouldn't be the quantization formula (in one dimension) equal to $N_{smooth}(E)+N_{osc}(E) = \oint_{C}p.dq$ ?? where the Oscillating term is just the correction from Gutzwiller trace formula or a ...
621 views

### Is the quantization of the harmonic oscillator unique?

To put it a little better: Is there more than one quantum system, which ends up in the classical harmonic oscillator in the classial limit? I'm specifically, but not only, interested in an ...
413 views

### Magnetic monopole and electromagnetic field quantization procedure

From the Maxwell's equations point of view, existence of magnetic monopole leads to unsuitability of the introduction of vector potential as $\vec B = \operatorname{rot}\vec A$. As a result, it was ...
418 views

### Some questions on observables in QM

1-In QM every observable is described mathematically by a linear Hermitian operator. Does that mean every Hermitian linear operator can represent an observable? 2-What are the criteria to say whether ...
82 views

163 views

### Quantum gravity at D = 3

Quantization of gravity (general relativity) seems to be impossible for spacetime dimension D >= 4. Instead, quantum gravity is described by string theory which is something more than quantization (...
822 views

### Virasoro constraints in quantization of the Polyakov action

The generators of the Virasoro algebra (actually two copies thereof) appear as constraints in the classical theory of the Polyakov action (after gauge fixing). However, when quantizing only "half" of ...
183 views

### How does one geometrically quantize the Bloch equations?

I've just now rated David Bar Moshe's post (below) as an "answer", for which appreciation and thanks are given. Nonetheless there's more to be said, and in hopes of stimulating further posts, I've ...