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 ...

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Is there any connection between “Lagrangian and Eulerian formalism of fluid” and “Heisenberg and Shrodinger picture”

Is there any connection between "Lagrangian and Eulerian formalism of fluid" and "Heisenberg and Shrodinger picture of Quantum mechanics"? Thanks!
1
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0answers
60 views

Does nonlocal theory violate causality?

Let's talk about two kinds of nonlocal theories. The first one frequently derives from integrating out part of the degrees of freedom to obtain a kind of effective theory. Probably, we get an integral ...
2
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1answer
45 views

Solving the 1-d time-independent Schroedinger's equation with an infinite boundary

In my introductory modern physics class we have examined time-independent solutions to the Schrödinger equation in 1 dimension. We looked at a few cases without finite boundary, e.g., free particles ...
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0answers
48 views

Sudden Approximation for Beta Decay of Tritium Atom

I am working out this problem right now, and I'm confused by the answers I'm getting. Problem: A tritium nucleus (Z = 1) in a tritium atom undergoes beta decay, i.e., a neutron in the nucleus emits an ...
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0answers
73 views

Could the phase factor $i$ be replaced by “matrix representation” totally in quantum mechanics? [duplicate]

It seems that $i$ plays an important role in quantum mechanics (Q.M.). On the other hand, linear algebra plays such an important role in Q.M. too. So would linear algebra, such as a matrix be able to ...
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0answers
54 views

Electromagnetic force interaction

As far as I know, the electromagnetic force only interacts on particles with electrical charge, but I was told that the electromagnetic force was involved in the following reaction: ...
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0answers
20 views

A question about Gell-Mann Low theorem?

Let $|\Psi_0\rangle$ be an eigenstate of $H_0$ with energy $E_0$ and let the 'interacting' Hamiltonian be $H=H_0 + gV$, where $g$ is a coupling constant and $V$ the interaction term. We define a ...
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0answers
90 views

A few questions about interacting quantum field?

In interacting quantum field, we think that interaction is adiabatic switch on/off. So in the infinite past, we can think there is no interaction, so we can have particle interpretion. There are four ...
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0answers
37 views

Quantum fluctuations in the non-relativistic limit

Is there any way to describe quantum fluctuations in ordinary quantum mechanics? For instance, a proton fluctuating into a proton-$\pi^0$ state and then back to a proton? What are the relevant ...
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2answers
136 views

The gauge covariant derivative and it's substitution

I was wondering wether it would make a difference (in general) if I were to were introduce the gauge covariant derivative $$D_\mu=\partial_\mu+ieA_\mu$$ In the Lagrangian density and then derive the ...
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0answers
29 views

Solve Eigenvalues for Particles enclosed in a hard surface?

Is there a way to calculate the energy eigenvalues for a particle enclosed in an impenetrable enclosing surface? I tried evaluating the Fourier transformation of the Laplacian operator \begin{align} ...
3
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1answer
154 views

Why have $n$, $\ell$, $m_\ell$, $m_s$ been picked as quantum number symbols *in this order*?

I’m learning about electron configurations and don’t quite understand why $n$, $\ell$, $m_\ell$, $m_s$ have been picked as symbols for the quantum numbers. As far as I understand it, the principal ...
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2answers
40 views

Total energy of a quantum gas

I'm dealing with a quantum gas, thought as a system of N non-interacting particles. I would be tempted to say that the total energy of the system equals the sum of the energies of the single ...
2
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2answers
114 views

electron in the nucleus

In the event that the electron is in nucleus of the atom (via tunneling effects and other things I don't understand), How does QED deal with this situation?
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0answers
17 views

Average value of consecutive measurements of two observables

Suppose we had two boxes named "1" and "2", and suppose we can measure observables $A_1$ and $A_2$ from these boxes, respectively. $A_1$ and $A_2$ commute, meaning we can find a basis of simultaneous ...
2
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2answers
106 views

Expectation Value of a Dynamical Variable

In quantum mechanics, we generally take about "expectation values of dynamical variables". However, by the postulates of quantum mechanics, every dynamical variable in quantum theory is represented by ...
3
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2answers
110 views
+50

Proving a step in this field-theoretic derivation of the Bogoliubov de Gennes (BdG) equations

In derivation of the BdG mean field Hamiltonian as follows, I have a confusion here in the second step: $H_{MF-eff} = \int ...
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0answers
24 views

Would superluminal signalling imply the violation of the No Cloning Theorem and unitarity?

The no-cloning theorem implies that we cannot use entanglement to send signals faster-than-light. Has anyone proved the contrapositive? That is, if we are given a system for superluminal signalling ...
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0answers
44 views

Why is the orbital angular momentum of a pi electron along the axis of two atoms' molecule one?

I'm reading quantum chemistry. The book says that the orbital angular momentum of a $\pi$ electron along the symmetry axis of a molecule made up of two atoms is $\pm 1$. I think this is a primary ...
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3answers
56 views

Help understanding proof in simultaneous diagonalization

The proof is from Principles of Quantum Mechanics by Shankar. The theorem is: If $\Omega$ and $\Lambda$ are two commuting Hermitian operators, there exists (at least) a basis of common eigenvectors ...
4
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1answer
81 views

What exactly does Aaron D. O'Connell's experiment show?

I watched a TED talk by the scientist Aaron D. O'Connell about actually seeing quantum superposition. The link to the talk is :- ...
2
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0answers
43 views

Spatial profile for a superconducting qubit's wavefunction

What is a spatial profile for a wavefunction of a superconducting qubit (such as say a flux qubit, charge qubit, or a transmon)? I am trying to calculate the energy shift of an superconducting qubit ...
1
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2answers
91 views

When combining three spin $\frac{1}{2}$ particles what are the corresponding states?

I want to combine three spin half particles and this is what I have so far. I used the lowering operator $J_{-}$ on the top states and found the following states fine: ...
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0answers
39 views

Angular momentum of 2d harmonic oscillator

So, I have the problem of determining the spectrum of H and L, in terms of creation and annihilation operators of angular momentum... The problem goes along with what is happening on this page. ...
4
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1answer
81 views

Symmetry and Degeneracy of Free Particles

Consider the hamiltonian $H=\frac{p_x^2}{2m}$ in 1-D. It is invariant under $p_x \rightarrow -p_x$. Again, this hamiltonian also has translational symmetry. Which one of these two is responsible for ...
2
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0answers
25 views

What is weak coupling of photon polarization to a pointer?

This question is refered to those who are familiar with the concept of weak measurement. In short: How can the polarization of a photon be coupled to the position of a pointer state? What is the ...
3
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1answer
77 views

Quantum mechanics and atomic bonding

I'm learning quantum mechanics in high school this year, and I have several doubts. I've done my research on various websites but my understanding is still fuzzy. I understand that when I punch a wall ...
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2answers
143 views

Does quantum randomness predicate an infinite number of realities?

I am a layman when it comes to physics and especially quantum mechanics. I have seen many documentaries on the subject, and often in these productions there is a physicist featured explaining the ...
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0answers
39 views

Simpler quantum “paradox” implying supraluminal connection

Executive summary: "Collapse of the wave function" is inherently supraluminal. I suggest an easier thought experiment to demonstrate the apparently supraluminal (or FTL) aspect of a quantum ...
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0answers
31 views

A small contradiction between periodic boundary condition and first Brilliouin zone

In condensed matter, one usually considers Bloch states inside the first Brilliouin zone, which, for 1d system with lattice constant $a$, is $-\pi/a<k<\pi/a$. But the basis of this, Bloch ...
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0answers
20 views

Uncertainty principle characterizing metallic bonding?

So I was trying to think through the statement that the uncertainty principle can characterize metallic bonding. I know that the uncertainty principle is: $\Delta p \Delta x = \frac{\hbar}{2}$. And ...
1
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1answer
35 views

Reflection of an evanescent matter wave within a finite barrier?

To my understanding if I have a finite barrier with potential $V(x)>E$, then to the left of the barrier, the wavefunction can be represented as two exponentials: $$\psi= e^{(ik_{left} x)} + ...
1
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1answer
115 views

Are we so sure about superposition?

Apparently particles can be anywhere when not observed. How strong is this theory really? Okay the wave-function can be collapsed through observation but how are we so sure that when an object is not ...
6
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2answers
125 views

Galilean, SE(3), Poincare groups - Central Extension

After having learnt that the Galilean (with its central extension) with an unitary operator $$ U = \sum_{i=1}^3\Big(\delta\theta_iL_i + \delta x_iP_i + \delta\lambda_iG_i +dtH\Big) + ...
2
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0answers
31 views

How to formulate collapse in polarization subspace of a photon?

I am wondering how to describe the collapse of a photon state when it is measured in the polarization degree of freedom (say by a filter which let pass just one particular polarisation). Let the free ...
-1
votes
1answer
79 views

Commutator with Pauli spin matrices and the momentum operator

How is $\left[\vec\sigma \cdot \vec p, \vec \sigma \right]$ proportional to $\vec \sigma\times \vec p$, where $\sigma$ are the Pauli spin matrices and $p$ is the momentum operator?
2
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0answers
78 views

The Uncertainty Principle and Energy Nonconservation

The uncertainty principle is listed in most textbooks and articles as $$ \Delta E \Delta t \geq \frac{\hbar}{2}.$$ This can be derived in many ways in many different settings, most of them involving ...
2
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0answers
43 views

Limits of integration for the radial wave function of the Hydrogen atom in the WKB approximation

I am working a problem where we have to find the energy eigenvalues for the radial wave function of the hydrogen atom for $\ell=0$ using the WKB approximation. I am sure that I set up the integral ...
3
votes
3answers
117 views

Can the expectation value of the square of momentum be negative?

I've been solving a problem in quantum mechanics, and I was deriving the standard deviation of $P$, knowing that $\langle P\rangle=0$. Because $\Delta P=\sqrt{\langle P^2 \rangle - \langle P \rangle ...
0
votes
1answer
60 views

Addition of Angular Momentum

I am tring to find the eigenvectors of a two spin system, with $j_1=3/2$ and $j_2=1/2$. To start, $$m_1 =-3/2,-1/2,1/2,3/2$$ $$m_2=-1/2,1/2$$ For $j_1$, there are 4 possible states, and 2 possible ...
2
votes
1answer
67 views

In the Dirac equation, do $\alpha$ and $p$ commute?

The Dirac Hamiltonian is given as $H = \vec \alpha·\vec pc + \beta mc^2$ , Do the alpha and beta operators commute with the momentum operator? If yes then how?
-1
votes
5answers
141 views

How does quantum world affect us and why should I care about it? [duplicate]

We live in a world which is much larger than quantum world. The laws of quantum physics are not valid. While I am pressing the keys on my laptop, I have 100% certainty that I am writing what I really ...
11
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1answer
143 views

Lie group of Schrodinger Wave equation

In Ballentine's book on quantum mechanics (in 3rd chapter), he introduces the symmetry transformation of Galilean group associated with Schrodinger equation. Now the Galilean group as such has 10 ...
2
votes
2answers
74 views

How to deal with mean field method in antiferromagnetism?

There are lots of ways to apply the mean field method to deal with the Ising model whose ground state is a ferromagnetic state. Hence, it is easy to find the order parameter named magnetization to ...
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0answers
61 views

Variational principle

In the LMTO method, the interstitial region is approximated by plane waves and the muffin tin region of the potential by solutions to the radial Schrodinger equation. In using the variational method ...
6
votes
2answers
169 views

Why $-i\hbar\vec\nabla$ for momentum in quantum mechanics, while $m\vec{v}$ in classical mechanics?

I am a little bit confused when thinking of the momentum representation in QM and CM. In QM, momentum is represented as $-i\hbar\vec\nabla$, while in classical, momentum is represented as $m\vec{v}$. ...
4
votes
1answer
125 views

Trace of an operator matrix (Quantum computation and quantum information)

I'm reading the book Quantum computation and quantum information by Mike & Ike and I'm stuck at 2.60/2.61. There, the author says that, given the operator $A|ψ⟩⟨ψ|$, its trace is: $${\rm ...
2
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1answer
71 views

Why is the camera not the culprit? [duplicate]

Perhaps I am completely wrong, but as I understand it our observation of a system can affect the outcome. The example I remember is the double slit experiment where electrons behave as a wave at ...
0
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2answers
72 views

Momentum Operator in Quantum Mechanics

1) What is the difference between these two momentum operators: $\frac{\hbar}{i}\frac{\partial}{\partial x}$ and $-i\hbar\frac{\partial}{\partial x}$? How are these two operators the same? My ...
3
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1answer
119 views

Understanding the Selection Rules of a Spin-Forbidden, Magnetic Dipole Transition in Molecular Oxygen

I am studying the transition from the second excited electronic state of molecular oxygen, $b^1\Sigma_g^+$ , to the ground state, $X^3\Sigma_g^-$. I know that the ground state has total angular ...