Tagged Questions
2
votes
1answer
60 views
Why we call the ground state of Kitaev model a Spin Liquid?
Now we always talk about the so-called Kitaev spin liquid. One important property of spin liquid is global spin rotation symmetry. Let $\Psi$ represents a spin ground state, if $\Psi$ has global spin ...
2
votes
1answer
53 views
Possible states for two electrons in the helium atom
Consider the helium atom with two electrons, but ignore coupling of angular momenta, relativistic effects, etc.
The spin state of the system is a combination of the triplet states and the singlet ...
2
votes
0answers
60 views
A general wavefunction in a square lattice
Suppose we have a square lattice with periodic condition in both $x$ and $y$ direction with four atoms per unit cell, the configuration of the four atoms has $C_4$ symmetry. What will be a general ...
3
votes
2answers
93 views
What is a symmetry of a physical system?
If I understand correctly, in many context in physics (quantum mechanics?), a physical system is specified by giving its Hamiltonian. I also hear that symmetries are rather essential.
As far as the ...
5
votes
2answers
160 views
A question on the existence of Dirac points in graphene?
As we know, there are two distinct Dirac points for the free electrons in graphene. Which means that the energy spectrum of the 2$\times$2 Hermitian matrix $H(k_x,k_y)$ has two degenerate points $K$ ...
1
vote
2answers
100 views
Eigenfunctions in periodic potential
For Hamiltonian $\operatorname H$ and lattice translation operator $\operatorname T$, if
$$\operatorname H\psi=E\psi, \qquad \operatorname T\psi=e^{ik\cdot R}\psi,$$
and
$$\operatorname ...
3
votes
2answers
286 views
Galilean invariance of the Schrodinger equation
I am only asking this question so that I can write an answer myself with the content found here:
http://en.wikipedia.org/wiki/User:Likebox/Schrodinger#Galilean_invariance
and here:
...
0
votes
2answers
186 views
Harmonic oscillator and Lorentz symmetry
There is a analog between harmonic oscillator $x=\frac{1}{\sqrt{2\omega}}(a+a^\dagger)$ and quantum field $\phi=\int dp^3\frac{1}{(2\pi)^3}\frac{1}{\sqrt{2\omega_p}}(a_p e^{ipx}+a^\dagger e^{-ipx})$, ...
7
votes
2answers
275 views
Conjugate Variables, Noether's Theorem and QM
What is the underlying reason that the same pairs of conjugate variables (e.g. energy & time, momentum & position) are related in Noether's theorem (e.g. time symmetry implies energy ...
1
vote
1answer
319 views
Schrödinger function: Separable wave function with even potential function of x
I have done the Problem 2.1 in Griffiths' quantum mechanics,
and it seems not making sense to me.
What if the wave function isn't symmetric at all?
Then obviously the proof doesn't work. The ...
1
vote
1answer
152 views
Symmetry and overlapping of ground states
In a quantum mechanics, there is the following formula to derive the zero energy $E_0$ of a perturbed Hamiltonian $$H = H_0 + V$$ knowing the zero energy $W_0$ of the free Hamiltonian $H_0$:
$$E_0 = ...
0
votes
0answers
45 views
Dilatations in non-relativistic QM and operator tranformation
I was looking at a QM textbook exercise dealing with dilatations, the transformations are $x \rightarrow x' = \lambda x$ transforming $|\psi\rangle$ into $|\psi'\rangle = ...
3
votes
1answer
256 views
Conservation Laws and Symmetries
Usually, in Quantum Mechanics, an observable is an operator on the space of the possible quantum states (labelled as $|\psi\rangle$). If this quantity is conserved, in the meaning that the associated ...
3
votes
1answer
325 views
Even and Odd States of a 1D finite potential well
Is it possible for a particle trapped in a 1D finite potential well to evolve from a even state to an odd state and vice-versa? Why?
0
votes
0answers
54 views
Working principle of symmetry operations of a system with given physical situations
In the book I read some explanations about symmetry of a system.
We can make an experiment using lambda particle, A^. A^ can disintegrate into one proton and one pion - A^ and proton have same spin ...
1
vote
2answers
226 views
Symmetries, Generators, Commutators and Observables
I'm learning about generators and conservation laws and have derived the equation (1)
$$[Q,A]=-i\hbar f(A)$$
which is satisfied by the observable generator $Q$ for a transformation group with ...
13
votes
1answer
601 views
Classical and quantum anomalies
I have read about anomalies in different contexts and ways. I would like to read an explanation that unified all these statements or point-views:
Anomalies are due to the fact that quantum field ...
1
vote
1answer
120 views
Searching the point group of symmetry
I am engaged in the field of quantum-chemical calculations using programs written by myself. I have found out that I have a problem in finding the point group symmetry of the molecule.
The first idea ...
3
votes
6answers
549 views
Time Reversal Invariance in Quantum Mechanics
I thought of a thought experiment that had me questioning how time reversal works in quantum mechanics and the implications. The idea is this ... you are going forward in time when you decide to ...
9
votes
2answers
276 views
When “unphysical” solutions are not actually unphysical
When solving problems in physics, one often finds, and ignores, "unphysical" solutions. For example, when solving for the velocity and time taken to fall a distance h (from rest) under earth gravity:
...
1
vote
1answer
198 views
Conserved quantum observables from symmetries *with density matrix*
I’ve read Ballentine where he derives the conserved observable operators (momentum, energy, ...) from symmetries of space-time.
Can I read up such a derivation in more detail somewhere else or even ...
2
votes
1answer
374 views
Weinberg's way of deriving Lie algebra related to a Lie group
I was reading the second chapter of the first volume of Weinberg's books on QFT. I am quite confused by the way he derives the Lie algebra of a connected Lie group.
He starts with a connected Lie ...
7
votes
1answer
75 views
Representation on Hilbert space of the product of two symmetry transformations
We know by Wigner's theorem that the representation of a symmetry transformation on the Hilbert space is either unitary and linear, or anti-unitary and anti-linear.
Let $T$ and $S$ be two symmetry ...
3
votes
0answers
116 views
Symmetries of separable potential
For separable potential, say $x^4+y^4$, its symmetry are degenerate.
Is that a generic case to every separable potential? I will explain my question:
The potential $x^4+y^4$ has $A_1, B_1, A_2, B_2, ...
10
votes
4answers
728 views
QM and Renormalization (layman)
I was reading Michio Kaku's Beyond Einstein. In it, I think, he explains that when physicsts treat a particle as a geometric point they end up with infinity when calculating the strength of the ...
7
votes
2answers
323 views
Groups acting on physics - a clarification on electrons and spin
My first question is fairly basic, but I would like to clarify my understanding. The second question is to turn this into something worth answering.
Consider a relativistic electron, described by a ...
11
votes
1answer
1k views
Schrödinger Equation
I am reading up on the Schrödinger equation and I quote
Because the potential is symmetric under $x\to-x$, we expect that there will be solutions of definite parity.
Could someone kindly explain ...
8
votes
2answers
884 views
Poincare group vs Galilean group
One can define the Poincare group as the group of isometries of the Minkowski space. Is its Lie algebra given either by the equations 2.4.12 to 2.4.14 (..as also given in this page - ...
5
votes
2answers
1k views
Relation between total orbital angular momentum and symmetry of the wavefunction
My question essentially revolves around multi-electron atoms and spectroscopic terms. I understand the idea that the total wavefunction for Fermions should be antisymmetric. Consider as an example, ...
5
votes
2answers
503 views
Expansion in spherical harmonics in cubic symmetry
suppose I have an electrostatic potential which I expand in spherical harmonics via
$$\sum_{l,m} A^l_m r^n P_l^{|m|}(\cos \theta) e^{im\varphi}$$
and I know that the field has cubic symmetry. Is ...
1
vote
1answer
977 views
Symmetric potential and the commutator of parity and hamiltonian
In one dimension -
How can one prove that the Hammiltonian and the parity operator commute in the case where the potential is symmetric (an even function)?
i.e. that [H, P] = 0 for V(x)=V(-x)
21
votes
4answers
2k views
What is the usefulness of the Wigner-Eckart theorem?
I am doing some self-study in between undergrad and grad school and I came across the beastly Wigner-Eckart theorem in Sakurai's Modern Quantum Mechanics. I was wondering if someone could tell me why ...
3
votes
1answer
691 views
Why must the deuteron wavefunction be antisymmetric?
Wikipedia article on deuterium says this:
The deuteron wavefunction must be
antisymmetric if the isospin
representation is used (since a proton
and a neutron are not identical
particles, ...
