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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Some question on the definition of flux in the projective construction?

Here I have some confusing points about the definition of flux in the projective construction. For example, consider the same mean-field Hamiltonian in my previous question, and assume the $2\times 2$ ...
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1answer
121 views

Some conceptual questions in BEC

In Bose-Einstein condensate (BEC), people often say there is a well defined macroscopic phase. What exactly the macroscopic phase is? (a phase factor $\mathrm{e} ^{i\phi}$ in a many-body wavefuction?) ...
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1answer
595 views

Eigenvectors of the angular momentum operator $S_x$ [closed]

For a spin of $\frac{1}{2}$ the angular momentum operator can be written as $\vec{S} = \frac{\hbar}{2} \vec{\sigma}$ in matrix form. Find the eigenvalues and eigenvectors of $S_x$ where $\sigma_x = \...
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179 views

Single photon double slit experiment

In the question Double Slit experiment with just one photon or electron, one of the answers says There have been experiments recently where one can detect which the slit the particle went through ...
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1answer
76 views

How does the following commutator for measured observables and this operator relation imply the following relation?

$$ \hat{\Omega}_j{(\tilde{q}_j)}=\Omega_j(\tilde{q}_j-\hat{q}_j) $$ $$ [\hat{q}_j,\hat{q}_l]=ik_{jl} $$ Implies $$ [\hat{q}_j,\hat{\Omega}_l]= \frac{\partial\Omega_l(\tilde{q}_l-\hat{q}_l)}{\...
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1answer
3k views

Ground State Wavefunction of Two Particles in a Harmonic Oscillator Potential

Question: Two identical, non-interacting spin-$1/2$ particles are in a 1D Harmonic Oscillator Potential. Their Hamiltonian is given by $$H=\frac{p_{1x}^2}{...
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1answer
143 views

Product of position eigenvectors at different times

I've been thinking about this, and it might sound like a stupid question, but I can't seem to find an answer anywhere, here goes: Whenever we calculate expecation-values between two position ...
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0answers
328 views

Interpreting a Hamiltonian in terms of 'hopping' operators

I am having some trouble interpreting a Hamiltonian in terms of "hopping" operators. The Huckel model for nearest neighbour interaction in graphene is given by $$H=-t\sum_\vec{R}|\vec R\rangle\...
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2answers
131 views

What happens to the physical properties of electrons after diffraction?

Particle Wave duality shows us that waves and particles are the same thing. Therefore electrons can be viewed as both particles and waves. The wave properties of electrons can be seen in the double ...
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1answer
352 views

Arbitrary Complex Powers of Ladder Operators

Given the following pair of operators $a$ and $a^{\dagger}$ that satisfy the usual bosonic CCR: $$[a,a]=[a^{\dagger},a^{\dagger}] = 0;\ [a,a^{\dagger}] = 1$$ For what values of $\alpha \in\mathbb C$ ...
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2answers
576 views

Some doubts about photons

I am reading Berkeley Physics Course vol. 4 (Quantum Mechanics) , chapter 4 (photons). (1) Section 46: book says: consider a typical photon emitted by the source. It can be regarded as a a wave ...
5
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1answer
451 views

Schrödinger equation for two particles in a 3D box?

This is not a homework question, just a question I have developed to get a better conceptual understanding of the results of the Schrödinger equation. If I had a 3D spherical container or radius R, ...
3
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1answer
4k views

Commutator $[\hat{p},F(\hat{x})]$ of Momentum $\hat{p}$ with a Position dependent function $F(\hat{x})$?

I heard from my GSI that the commutator of momentum with a position dependent quantity is always $-i\hbar$ times the derivative of the position dependent quantity. Can someone point me towards a ...
3
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1answer
158 views

Classical dynamics with Schrodinger equation

What are some interesting classical systems for which the dynamics can be reduced to a many-body Schrodinger equation, at least in some useful regions of phase space, and in particular, with many ...
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3answers
848 views

How to derive the uncertainty relation for a system of arbitrary potential?

I've been trying to understand the derivation of the uncertainty principle for the harmonic oscillator as described here (see pages 100-101). What I don't understand is how the potential for the ...
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2answers
78 views

Difference between a central potential that is a point and one that is a sphere?

In quantum physics there is a special case known as a particle in a spherically symmetric potential. I have a problem which is similar to the case of a hydrogen atom in that there is one free electron,...
3
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1answer
217 views

What does $|x⟩|0⟩$ actually mean in bra-ket notation?

Consider the following quote from Wikipedia's page on Shor's algorithm: Initialize the registers to $Q^{-1/2} \sum_{x=0}^{Q-1} \left|x\right\rangle \left|0\right\rangle$ where $x$ runs ...
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1answer
283 views

A commutation problem in Hubbard model

Does the Hubbard Hamiltonian $$H=-t\sum_{\langle ij\rangle \sigma}c_{i\sigma}^{\dagger}c_{j\sigma}+h.c.+U\sum_{i}n_{i\uparrow}n_{i\downarrow}$$ commute with $\sum_{i}\mathbf{S}_i^2$? where $\mathbf{S}$...
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6answers
231 views

Meaning of probability in a multiverse/a many-world interpretation?

Consider me tossing a coin and I got tail as a result on observing it. Then, what would be the result of the 'parallel me' in another universe? If the 'parallel me' gets head as a result then, ...
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0answers
69 views

How does linearity of a measurement imply that the commutator of all measured observables are $c$-numbers?

I really don't understand with the linearity conditions I have where this comes from.
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1answer
174 views

Understanding operations of quantum computing advantages

For example, let us examine the case of quantum (discrete) fourier transform. There are $2^N$ samples. How do we initialize these $2^N$ samples into $N$ qubits? I have a hard time understanding this.
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5answers
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How to get the position operator in the momentum representation from knowing the momentum operator in the position representation?

I know that $$\tag{1}\hat{p}~=~-i\hbar \frac{\partial}{\partial x}~.$$ How can I get $$\tag{2}\hat{x}~=~i\hbar \frac{\partial}{\partial p}~?$$ I think this simple and I'm just over thinking it, ...
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5answers
992 views

When is energy discrete/quantized for a potential well?

Specifically, my question is: Should one expect energy quantization for a particle in the following potential well? More generally, how can one tell whether or not energy should be discrete/...
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1answer
289 views

Revisiting the microscopic concept of Touching with some more questions

This question is regarding the amazing answer given by Terry Bollinger at this Phys.SE post. I think this answer is very helpful but i do have some standing questions. He says Once the bonding ...
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1answer
291 views

Uncertainty principle in atomic clocks?

How does the uncertainty principle limit the accuracy of atomic clocks. I know line width and measurement time are important but not exactly why?
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1answer
483 views

Coercivity of a ferromagnetic material?

I understand that coercivity is the field/force required to demagnetize/magnetize a ferromagnetic material. What if we had two opposite magnetic fields of different strengths values H acting on the ...
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1answer
317 views

Paradox in the Hellmann-Feynman Theorem

The Hellmann-Feynman Theorem says $$\tag{1} \frac{d E_\lambda}{d \lambda} ~=~ \bigg\langle \psi(\lambda) \bigg| \frac{d H_\lambda}{d \lambda} \bigg| \psi(\lambda) \bigg\rangle$$ where $H_\lambda$ is a ...
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1answer
897 views

What is the correct Hamiltonian for a system of coupled quantum oscillators?

The Hamiltonian (see Eqn. 1 in Appendix 2 of this paper) for a system of coupled quantum oscillators is given as $$H=\frac{1}{2}∑_{i}p^{2}_{i}+\frac{1}{2}∑_{j,k}A_{jk}q_{i}q_{k}$$ Yet, in my QM ...
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0answers
300 views

QFT as a rigorous mathematical theory [duplicate]

I understood that quantum field theory is essentially based on a problematic mathematical basis. Can someone please explain what is the fundamental problem to formulate QFT as a rigorous mathematical ...
8
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3answers
5k views

What made Bohr quantise angular momentum and not some other quantity?

Bohr's second postulate in Bohr model of hydrogen atom deals with quantisation of angular momentum. I was wondering, though: why did he quantise angular momentum instead of some other quantity?
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0answers
101 views

How functions become operators in quantum mechanics? [duplicate]

What used to be functions in the context of classical mechanics like position, linear momentum, angular momentum, etc in quantum mechanics are operators (these operators act on the state to get ...
3
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2answers
305 views

The meaning of potential in Bohm-Aharonov experiment

The Bohm-Aharonov experiment involves a magnetic field inside a cylinder which is zero outside that cylinder. Nonetheless it affects the electrons moving outside the cylinder. The explanation for this ...
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1answer
72 views

Quantum Box and Quantum Number

How many quantum numbers are needed to describe a stationary state of a particle in a multi-dimensional quantum box (say 73)?
3
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0answers
106 views

The relation between the action of tunneling and the energy

In the semi-classical physics, the probability of the penetration through a barrier is given by $$ p \sim \exp \left( - A_{0} (E) \right), $$ where $A_0$ is the imaginary part of the action and $E$ ...
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5answers
1k views

Does an electron move from one excitation state to another, or jump?

I'm wondering, when an electron changes state, does it move from one state to another over some (very small) time period? Or does it change from one state to another in no time? If the former, what ...
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1answer
1k views

What are the “strong”, “ultrastrong” and “deep strong” coupling regimes of the Rabi model?

The Rabi model describes a two-level system interacting via a linear coupling with a quantized harmonic oscillator, and it is described by the hamiltonian $$ H_{\rm{Rabi}}=\hbar\omega\, a^\dagger a +\...
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1answer
526 views

What happens to entangled particles when momentum is measured?

In Wikipedia it is mentioned that position and momentum can be entangled as well as spin and polarization etc. I assume etc. is charge etc. I understand how if you measure spin up on one of a pair you ...
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2answers
1k views

Bound state in a potential well?

Reading from http://quantummechanics.ucsd.edu/ph130a/130_notes/node151.html It says: This means that the solutions separate into even parity and odd parity states. We could have guessed this from ...
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0answers
164 views

Some fundamental results in QFTs [closed]

In quantum theory we have some principles that guides us, e.g. Pauli's principle. What I am after in this question is a list of fundamental results, be it equation or identities that must hold in a ...
2
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1answer
155 views

What is the spin state of a spin-1/2 particle when it comes out of a Stern-Gerlach apparatus?

Having a particle entering the apparatus with spin state $|+\rangle$, for which $\hat S_x|+\rangle=+\frac\hbar 2|+\rangle$, I have a question about how to express the spin state when it comes out. I ...
11
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2answers
759 views

How are anyons possible?

If $|ψ\rangle$ is the state of a system of two indistinguishable particles, then we have an exchange operator $P$ which switches the states of the two particles. Since the two particles are ...
0
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1answer
173 views

Did physicists solve the grandfather paradox? [duplicate]

Now, physicists are trying to send information backward in time. But, why are physicists almost sure that this would happen and why are they so confident about it? Did physicists solve the grandfather ...
2
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1answer
350 views

Massless spin 1/2 particle

Could a massless spin 1/2 particle, or more generally massless half-integer spin particles exist? Does it make sense to say that they could be described for example by the Dirac equation by forgetting ...
3
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1answer
156 views

Negative energy solutions Dirac equation without radation field

In the book "Relativistic Quantum Mechanics" by Bjorken and Drell in Chapter 5.1 page 64 there is the following statement about the problem of negative solutions to the Dirac equation: By their ...
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2answers
236 views

Do any other particles get excited(or absorb energy) by photons like electrons?

Electrons get excited to different energy levels when photons of specific frequencies fall on them.But, is there other particles which absorb the energy of the photons?
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2answers
79 views

Which number should I suppose to $a$ (width of well) and $m$ (mass of particle) in potential well problem? [closed]

I tried to plot a complete of state functions of potential well problem but graph was so weird. I thought a cause was variables a and ...
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1answer
1k views

Dirac field and stress-energy tensor density

I read somewhere that stress-energy tensor density is a symmetric tensor. But if I take the Dirac Field tensor: $$T^{\mu \nu}=i \psi^\dagger \gamma^0 \gamma^\mu \partial^\nu \psi $$ How could I ...
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1answer
51 views

Reversed freezing point

Helium-3's Phase diagram shows that at the right temperature and pressure combination, the solid region dips downward as temperature increases. That means that you can heat it up and it will freeze. ...
6
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3answers
2k views

What is a Zero-Phonon Line (ZPL)?

I am trying to understand the electronic structure of the negatively charged NV centre in diamond, where there is a so-called Zero-Phonon Line (ZPL) in the spectrum. Can anybody explain what a ZPL is?
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2answers
638 views

Area under the graph of squared wave function

I was given a graph of square of the wave function of a hydrogen atom, against the distance of the electron from the nucleus (denoted by r). What I know is that the square of the wave function gives ...