Quantum mechanics describes the microscopic properties of nature in a regime where classical mechanics no longer applies. It explains phenomena such as the wave-particle duality, quantization of energy and the uncertainty principle and is generally used in single body systems. Use the quantum-field-...

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458 views

Is the spin-rotation symmetry of Kitaev model $D_2$ or $Q_8$?

It is known that the Kitaev Hamiltonian and its spin-liquid ground state both break the $SU(2)$ spin-rotation symmetry. So what's the spin-rotation-symmetry group for the Kitaev model? It's obvious ...
2
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3answers
309 views

Natural units of information

In physics entropy is usually measured in nats. I wonder is there a possible model of a physical system which has entropy of discrete number of nats? How particles and degrees of freedom should be ...
1
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1answer
123 views

Wigner friend experiment

Let's supposed we take the Wigner's friend experiment from the metaphysical arena and try to implement it as an actual physical experiment Assuming Wigner's lab friend is kept as a coherent ...
2
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1answer
190 views

S-Matrix, String theory, Matrix mechanics and Quantum Mechanics

I'm trying to learn theoretical physics up to string theory. I know linear algebra, calculus 1+2, complex analysis. I know the basics of homology, homotopy, group theory and differential geometry. Now ...
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1answer
3k views

Can electron exist as a standing wave inspite of successive superposition?

With the development of quantum mechanics, it was found that the orbiting electrons around a nucleus could not be fully described as particles, but needed to be explained by the wave-particle duality. ...
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2answers
191 views

What events lead to quantum decoherence?

Is there a very specific definition for all types of events where quantum decoherence occurs? Is it merely any event that is "thermodynamically irreversible" and/or "causes entropy to increase"? Is it ...
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3answers
486 views

Double-slit expirement fundamentals (half-silvered mirror version)

In the double-slit experiment variation in which 2 half-silvered mirrors and 2 mirrors are used to illustrate the interference of a stream of photons or single photons at a given time step, how is it ...
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2answers
256 views

Is there is a reason for Pauli's Exclusion Principle?

As a starting quantum physicist I am very interested in reasons why does Pauli's Exclusion Principle works. I mean standard explanations are not quite satisfying. Of course we can say that is because ...
3
votes
2answers
277 views

Wavefunction of an electron

Electron is a spin $\frac{1}{2}$ particle, so needs 2-component wave function but the Dirac theory of electron is based on 4-component wave function, are all components of it independent or only two ...
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3answers
202 views

Discrete movement vs wave function collapse

I remember once, as a child, thinking that objects do not really "move," but that at a very small scale they would have to "disappear" and then "appear" again at their newly shifted position, just the ...
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0answers
126 views

Geometric quantization AND nuclear physics

Classical mechanics has a natural mathematical setting in symplectic geometry and it may be asked if the same is true for quantum mechanics. Geometric quantization is one formalization of the notion ...
3
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1answer
81 views

How can I integrate in $\mathrm{d}t$ the cube of the harmonic oscillator propagator?

I'm redoing the calculations of "Point Canonical Transformations in the path integral", by Gervais and Jevicki; while doing so I stumbled in integrals like $$ \int \mathrm{d}t \, \Delta_F^3(t) = -\...
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1answer
359 views

Do Cooper pairs act like Cheshire cats?

Could the pairing up of electrons be explained by their spin being in a different position? What would separating the spin from an electron in matter do in theory?
5
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1answer
123 views

Do we have a fundamental Hamiltonian for the system of H$_2$O molecules?

From the quantum mechanics(QM) viewpoint, does there exist a Hamiltonian $H$ for the system of H$_2$O molecules? Assume that the number of H$_2$O molecules is fixed. Imagine that by calculating the ...
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0answers
82 views

How to prove the equivalence of two definitions of the scattering cross section

I have noticed that there are two definitions of differential scattering cross section in non-relativistic quantum mechanics. One of them is the most popular, particularly it is used in the book of ...
2
votes
2answers
445 views

Is the spin 1/2 rotation matrix taken to be counterclockwise?

The spin 1/2 rotation matrix around the $z$-axis I worked out to be $$ e^{i\theta S_z}=\begin{pmatrix} \exp\frac{i\theta}{2}&0\\ 0&\exp\frac{-i\theta}{2}\\ \end{pmatrix} $$ Is this taken to ...
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1answer
171 views

Addition of spin?

There is something I don't fully understand. When I have a problem like this: Let's look at a system with $j_1=1$ and $j_2=2$ spins. Let our system be in the state in which the total spin is $2$ and ...
4
votes
1answer
334 views

Did the Goudsmit-Uhlenbeck analysis of spin consider relativity?

It's frequently mentioned in introductory quantum mechanics texts that Goudsmit and Uhlenbeck conjectured that the magnetic moment of an electron was due to angular momentum arising from the electron ...
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2answers
917 views

Quantum Quench Problem

I read about the quantum quench problem in condensed matter physics. But what does really mean? Has anybody a good explanation about the origin of quantum quench problem?
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2answers
1k views

Is the Dirac Lagrangian Hermitian?

I'm wondering of the Dirac Lagrangian density $$\mathcal{L} =\overline{\psi}(-i\gamma^\mu \partial_\mu +m)\psi $$ is an hermitian operator, since upon complex conjugating one gets $$\mathcal{L}^\...
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1answer
99 views

Are all natural processes that are bigger than a molecule also deterministic? [closed]

Is there something bigger than a molecule and still random in nature? I know that the decay of an unstable atom cannot be predicted, only the probability of decay can be calculated. Molecules moving ...
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0answers
107 views

Wavefunctions of different observable values are orthogonal because for any state one of them equals zero. Right?

I'm trying to understand correspondence between observables and quantum operators. Let's assume that $\phi_1$ and $\phi_2$ are wavefunctions that can be obtained after the measurement of some ...
7
votes
4answers
497 views

Can we safely assume $\Psi(x,t) = \psi(x)e^{-i\omega t}$ always in QM?

In the particle in a box, harmonic oscillator and in Hydrogen Atom, we can safely assume $$\Psi(x,t) = \psi(x)e^{-i\omega t}.$$ So why not make it a postulate to consider the wave function to be ...
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2answers
155 views

Quantum eraser double slit experiment

In the quantum eraser double slit experiment, does the photon (or wavefunction) pass through one slit or both slits when different polarizers are placed over the slits?
6
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5answers
2k views

Example of the time-independent Schrödinger equation having a complex solution?

We know $\Psi(x,t)$ is complex, but can $\Psi(x)$ be complex? I have seen particle in a box, well and harmonic oscillator. All have real solutions for time-independent Schrödinger equation. Hence, I ...
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1answer
119 views

What if Correspondence principle in QM happening in classical sense? [closed]

I assume a simple set up (hope to generalize it later)... suppose there is a position pdf (need not be position but any) (probability density function) which is the magnitude of a $\Psi(x)$ predicted ...
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1answer
197 views

relation between Schrodinger equation and wave equation [duplicate]

I have always been confused by the relationship between the Schrödinger equation and the wave equation. $$ i\hbar \frac{\partial \psi}{\partial t} = - \frac{\hbar^2}{2m} \nabla^2+ U \psi \hspace{0....
7
votes
1answer
451 views

Virial theorem and variational method: a question

I have an hydrogenic atom, knowing that its ground-state wavefunction has the standard form $$ \psi = A e^{-\beta r} $$ with $A = \frac{\beta^3}{\pi}$, I have to find the best value for $\beta$ (...
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0answers
42 views

Why is a coherent state an eigenfunction to the annihilation operator? [duplicate]

In class when we talked about the harmonic oscillator in QM we noticed that the eigenfunctions to the annihilation operator are coherent states in the sense that they have minimum uncertainty in ...
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2answers
2k views

Particle in a 1-D box and the correspondence principle

Consider the particle in a 1-d box, we know very well the solutions of it. I'd like to see how the correspondence principle will work out in this case, if we consider position probability density ...
2
votes
2answers
379 views

Wave function for an electron in and around a small charged sphere

I am interested in solutions of the Schroedinger equation. For simplicity I started my studies with the $n=1$ ground state of the hydrogen atom. I was particularly interested in the higher moments of ...
13
votes
5answers
993 views

The strange thing about the maximum in Planck's law

I read that it makes a difference whether you calculate $\frac{dE(\lambda) }{d \lambda}=0$ or $\frac{dE(\omega)}{d \omega}=0$ in the sense that the maximum energy density with respect to the ...
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4answers
625 views

Why complex functions for explaining wave particle duality?

I have this very bad habit of going to the scratch, discarding all the developments of a theory and worldly knowledge, and ask some fundamental (mostly stupid and naive, as some may say) questions as ...
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0answers
151 views

on quantum steering

I have become interested in quantum steering after listening a talk and tried to read more about it. I think I am more confused now. My understanding is as follows: Sharing a (entangled) state, ...
2
votes
1answer
162 views

Infinitely many soft photons from pushing an electron?

I have been looking at some of the archives here and seen it quoted by Ron Maimon , that pushing an electron with a classical field means the electron will produce infinitely many soft photons should ...
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0answers
143 views

Quantum Eraser under Lorentz Boost

Suppose I am conducting the Quantum Eraser experiment. The results of this experiment are easy to understand with the traditional quantum mechanical interpretation of a pair of entangled photons. ...
0
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1answer
295 views

Triangle inequality Clebsch-Gordan coeffcients

The Clebsch-Gordan coefficients can only be non-zero if the triangle inequality holds: $$\vert j_1-j_2 \vert \le j \le j_1+j_2$$ In my syllabus they give the following proof: $$-j \le m \le j$$ $$-j_1 ...
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0answers
115 views

The status of unobservable quantum mechanical predictions

Orthodox quantum mechanics intrinsically requires an observer - since the only connection from the mathematical formalism to physical reality is through the measurement axiom (probability of observing ...
4
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1answer
342 views

Total angular momentum operator forms a complete set? (Clebsch-Gordan coefficients)

While introducing Clebsch-Gordan coefficients, they state that the operators: $$ \vec{J_1}^2,\vec{J_2}^2,J_{1z},J_{2z}$$ form a complete set of compatible observables. Which means that there is no ...
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0answers
99 views

The nature of the probability distribution for the energy of a photon released via stimulated emission

The vanilla description of stimulated emission (e.g. in the context of an inverted population laser gain medium) says that a photon with some state vector specifying its energy / polarization / ...
3
votes
4answers
202 views

What aspect of quantum mechanics forces probabilities to be (conventionally, at least) central?

I understand how to compute probability distributions and expected values and such from quantum states, but a lot of treatments of QM make it look like this is what the wavefunction is essentially for....
2
votes
0answers
112 views

current density in 1-d

I have a slight problem with the notion of the current density in one dimension. For example the probability current in 1-d given by: $J(x) = -\frac{1}{m} Im(-i\psi^*\partial_x \psi)$ calculation the ...
4
votes
3answers
1k views

Comparison of 1D and 3D wave functions

When discussing the Schroedinger equation in spherical coordinates, it is standard practice in QM handbooks to point out that the radial part of the 3-dimensional wave equation bears a strong analogy ...
5
votes
1answer
296 views

Photons traveling backwards in time?

Imagine that two widely separated charged particles $A$ and $B$ exchange a photon. Because they are far apart one can imagine that there is a major contribution to the photon propagator that travels ...
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2answers
3k views

Why can't a spin-1 particle decay into two identical spin-0 particles?

I've got this far: Suppose a spin-1 particle with $j$,$l$,$s$ decays into a system of two identical spin-0 particles with $J$,$L$,$S$. The RHS must have total spin $S=0$, so $J=L$ which must be even ...
0
votes
1answer
107 views

Quantum physics and object location

If I understand correctly, according to quantum physics, subatomic particles can "leap" from one location to another (for example, from a location on earth to a location on the "other side" of the ...
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2answers
297 views

Separation of variables in various PDEs, physical meaning

The method of separation of variables produces an undetermined separation constant and a family of solutions indexed by the values of this constant. For instance, in the case of an infinitely long ...
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2answers
3k views

Nuclear Spin of Sodium 23

I am actually calculating the nuclear spin of Sodium 23. Here we have 11 protons and 12 neutrons. Now both the nuclei are short of the magic numbers. When I use the shell model for protons and ...
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2answers
284 views

Is the sign in the Schrodinger equation physical?

I always have trouble remembering the sign in factors like $\exp(\pm ik\cdot x)$ (I'll use mostly minus signature here) that arise in field theory. My mnemonic is to remember that the Schrodinger ...
4
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3answers
323 views

Some small questions about quantum spin and rotations

I'm studying about quantum-spin (in a syllabus about non-relativistic quantum-mechanics though), but I have some trouble understanding everything. So I would like to ask some small questions, which ...