Tagged Questions
4
votes
2answers
145 views
Integer physics
Are there interesting (aspects of) problems in modern physics that can be expressed solely in terms of integer numbers? Bonus points for quantum mechanics.
5
votes
2answers
168 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 ...
0
votes
0answers
17 views
Allowed Quantum States- Filkelstein and Rubinstein constraints
So basically i'm doing a report on Finkelstein and Rubinstein constraints. I have a system where the allowed quantum states satisfy ...
2
votes
4answers
183 views
What entities in Quantum Mechanics are known to be “not quantized”?
Since all the traditional "continuous" quantities like time, energy, momentum, etc. are taken to be quantized implying that derived quantities will also be quantized, I was wondering if Quantum ...
6
votes
0answers
220 views
exponential potential $ \exp(|x|) $
For $a$ being positive what are the quantization conditions for an exponential potential?
$$ - \frac{d^{2}}{dx^{2}}y(x)+ ae^{|x|}y(x)=E_{n}y(x) $$
with boundary conditions $$ y(0)=0=y(\infty) $$
I ...
3
votes
2answers
165 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 ...
6
votes
1answer
169 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.
1
vote
1answer
195 views
Quantization of Nambu–Goto action in multiples of Planck's constant?
Isn't it possible? Quantization of Nambu–Goto action
$$\mathcal{S} ~=~ -\frac{1}{2\pi\alpha'} \int \mathrm{d}^2 \Sigma \sqrt{{\dot{X}} ^2 - {X'}^2}~=~nh\qquad n \in\mathbb{Z}.$$
12
votes
4answers
572 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 ...
0
votes
0answers
135 views
Bohr sommerfeld quantiztion rule and Gutzwiller trace
assuming we can evaluate the eigenvalue staircase $ N(E) $ in both manners with the Bohr-Sommerfeld quantization rule
$ N(E)2\pi \hbar = \oint _{C}p.dq $
and using the Gutzwiller trace $ N(E)= ...
3
votes
2answers
840 views
Bohr Model of the Hydrogen Atom - Energy Levels of the Hydrogen Atom
Why the allowed (stationary) orbits correspond to those for which the orbital angular momentum of the electron is an integer multiple of $\hbar=\frac {h}{2\pi}$?
$$L=n\hbar$$
Bohr Quantization rule of ...
2
votes
1answer
179 views
Computing a density of states of Hamiltonian $ H=xp$
How could I compute the integral
$$ N(E)~=~ \int dx \int dp~ H(E-xp) $$
the 'Area' inside the Phase space is taken for $ x \ge 0 $ and $ p\ge 0 $? The result should be
$$ N(E)~=~ ...
1
vote
0answers
69 views
shouldn't we add the oscillating terms into Bohr-Sommerfeld quantization formula
shouldn't be the quantization formula (in one dimension) equal to
$ N_{smooth}(E)+N_{osc}(E) = \oint_{C}p.dq $ ??
where the Oscillating term is just the correction from Gutzwiller trace formula or a ...
7
votes
3answers
294 views
Is the quantization of the harmonic oscillator unique?
To put it a little better:
Is there more than one quantum system, which ends up in the classical harmonic oscillator in the classial limit?
I'm specifically, but not only, interested in an ...
5
votes
3answers
313 views
Some questions on observables in QM
1-In QM every observable is described mathematically by a linear Hermitian operator. Does that mean every Hermitian linear operator can represent an observable?
2-What are the criteria to say whether ...
7
votes
1answer
66 views
How does one geometrically quantize the Bloch equations?
I've just now rated David Bar Moshe's post (below) as an "answer", for which appreciation and thanks are given.
Nonetheless there's more to be said, and in hopes of stimulating further posts, I've ...
9
votes
3answers
368 views
Rigorous proof of Bohr-Sommerfeld quantization
Bohr-Sommerfeld quantization provides an approximate recipe for recovering the spectrum of a quantum integrable system. Is there a mathematically rigorous explanation why this recipe works? In ...
14
votes
2answers
124 views
Geometric quantization of identical particles
Background:
It is well known that the quantum mechanics of $n$ identical particles living on $\mathbb{R}^3$ can be obtained from the geometric quantization of the cotangent bundle of the manifold ...
2
votes
2answers
249 views
Trouble with constrained quantization (Dirac bracket)
Consider the following peculiar Lagrangian with two degrees of freedom $q_1$ and $q_2$
$$ L = \dot q_1 q_2 + q_1\dot q_2 -\frac12(q_1^2 + q_2^2) $$
and the goal is to properly quantize it, following ...
15
votes
7answers
1k views
Does Quantum Mechanics assume space and time are continuous?
I was confused when I was listening to a Quantum Mechanics lecture online. Are space and time assumed to be continuous or discrete in Quantum Mechanics?
I can see the question is vague, but this is ...
