2
votes
1answer
106 views
Indistinguishable particles in quantum mechanics
If you have two particles of the same species , Quantum mechanics says that $\Phi_{m_{1},x_{1},p_{1},m_{2},x_{2},p_{2}}=\alpha\Phi_{m_{2},x_{2},p_{2},m_{1},x_{1},p_{1}}$
But I don't understand why ...
0
votes
0answers
22 views
Constructing a Toffoli gate from CNOT and single-qubit gates
Toffoli gate in terms of CNOT and single-qubit gates.
Thanks much!
6
votes
2answers
83 views
Must a vertical sundial face exactly South?
I am a sundial. I'm prepared to bet
Your watch can't tell when the sun will set
I once heard Frank King talk about sundials in particular this very cool one, which measures Babylonian hours ...
2
votes
0answers
55 views
How to define the mirror symmetry operator for Kane-Mele model?
Let us take the famous Kane-Mele(KM) model(http://prl.aps.org/abstract/PRL/v95/i22/e226801 and http://prl.aps.org/abstract/PRL/v95/i14/e146802) as our starting point.
Due to the time-reversal(TR), ...
2
votes
7answers
233 views
Electrostatic Potential Energy Derivation
How is the boxed step , physically as well as mathematically justified and correct ?
Source:Wiki http://en.wikipedia.org/wiki/Electric_potential_energy
As work done = $- \Delta U $. for Conservative ...
7
votes
3answers
129 views
Trace and adjoint representation of $SU(N)$
In the adjoint representation of $SU(N)$, the generators $t^a_G$ are chosen as
$$ (t^a_G)_{bc}=-if^{abc} $$
The following identity can be found in Taizo Muta's book "Foundations of Quantum ...
1
vote
1answer
34 views
Topological phase transitions - breaking of continuous translational invariance
I'm relatively new to the theoretical side of physics. I have a question about topology, continuous symmetry breaking and phase transitions. Your help is much appreciated!
Ok so I have an infinite ...
0
votes
1answer
96 views
Einstein and vibrational energy of the atom and its way to QM
As suggested by one of the commentators on my last question, I am going through Bohr's Nobel prize lecture in order to understand how quantum mechanics was developed.
The lecture describes Planck's ...
1
vote
1answer
26 views
Volume of gas at which relative fluctuation of gas density occurs
I have the following question:
In what volume of gas occurs 10 % relative fluctuation of gas density
under pressure of $10^5\text{ Pa}$ and temperature of $293.15\text{ K}$?
I don't understand ...
1
vote
0answers
15 views
What is a good reynolds number for this process?
I’m trying to convince my boss that the mixers we are using are too much. I’m trying to prove that we are over-mixing our product. Our product is ink…just your basic ink found in your printer at home. ...
1
vote
1answer
15 views
Finding the Steady State Charges
Here the problem states to find the steady state charges on the condensers.
But here the capacitor have a resistance in parallel connection , so how can we distribute the potential drop across ...
3
votes
2answers
67 views
First and second fundamental forms
I'm writing notes about the 3+1 formalism in general relativity, for myself. Inevitably I came across the notions of first and second fundamental forms. Mathematically, it is clear how these objects ...
2
votes
1answer
57 views
sine-Gordon equation
I have derived a solition equation (2 dimensions) from scalar field theory $$\varphi(x) = v\tanh\Bigl(\tfrac{1}{2}m(x - x_0)\Bigr),\tag{1}$$
and also I have got sine-Gordon equation for solition
...
0
votes
0answers
34 views
A question to the theory of multiverse
Guys I couldn't catch a point of multiverse theory..
Theory: If space-time goes on forever, then it must start repeating at some point, because there are a finite number of ways particles can be ...
1
vote
0answers
60 views
How to calculate Riemann and Ricci tensors for a sphere? [closed]
Let's have the metric for a sphere:
$$
dl^{2} = R^{2}\left(d\psi ^{2} + sin^{2}(\psi )(d \theta ^{2} + sin^{2}(\theta ) d \varphi^{2})\right).
$$
I tried to calculate Riemann or Ricci tensor's ...
