Questions tagged [quantum-mechanics]

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-theory tag for the theory of many-body quantum-mechanical systems.

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Experimental test of the non-statisticality theorem?

Context: The paper On the reality of the quantum state (Nature Physics 8, 475–478 (2012) or arXiv:1111.3328) shows under suitable assumptions that the quantum state cannot be interpreted as a ...
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Orbits of maximally entangled mixed states

It is well known (Please, see for example Geometry of quantum states by Bengtsson and Życzkowski ) that the set of $N$-dimensional density matrices is stratified by the adjoint action of $U(N)$, where ...
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Is there a physical interpretation to invariant random matrix ensembles?

Disclaimer. I am a graduate student in pure mathematics, so my knowledge of physics more advanced than basic 1st/2nd year undergraduate physics is very limited. I welcome corrections on any ...
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21 votes
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Does the Mott insulator exist?

The Mott insulator is a system that, due to strong electron-electron interactions, is an insulator but is expected to be a metal by formal charge counting of electrons in the unit cell. Often, the ...
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Criteria for being able to work with gravity in quantum mechanics, without a full theory of quantum gravity?

It's common to see people oversimplify by saying that physics currently lacks the tools to describe any situation involving both quantum mechanics and gravity. Clearly this is not the case. For ...
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15 votes
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How does one compute the state of a quantum system following imperfect measurement?

Suppose I have a quantum system $S$ ("system") with Hamiltonian $H_S$ and initial density matrix $\rho_S(0)$. I allow $S$ to interact with another system $P$ ("probe"), which has Hamiltonian $H_P$ and ...
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Why do flux qubits have to be micrometer-sized?

Flux qubits are made using micrometer sized Josephson junctions. They exploit superconducting properties to create and interfere with the magnetic flux between them. My question is that I've seen ...
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14 votes
1 answer
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How can I write a Gaussian state as a squeezed, displaced thermal state?

I would like to write a Gaussian state with density matrix $\rho$ (single mode) as a squeezed, displaced thermal state: \begin{gather} \rho = \hat{S}(\zeta) \hat{D}(\alpha) \rho_{\bar{n}} \hat{D}^\...
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13 votes
3 answers
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To what extent can one recover plane waves from the Airy eigenfunctions of a linear potential as the field is turned off?

Consider a single massive particle in one dimension under the action of a static linear potential, with the hamiltonian $$ \hat H=\frac{\hat p^2}{2}+\hat{x}F_0. $$ The eigenstate at energy $E$ is, ...
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Topological entanglement entropy only defined for a system in the ground state?

What happens to the topological entanglement entropy of a system, when it is driven out of its groundstate by increasing the temperature?
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Is the helium atom with only a contact interaction between the electrons solvable?

Consider the hamiltonian for a helium atom, $$ H=\frac12\mathbf p_1^2+\frac12\mathbf p_2^2 - \frac{2}{r_1}-\frac{2}{r_2} + a \, \delta(\mathbf r_1-\mathbf r_2), $$ where I have taken out the ...
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Sequential Stern-Gerlach devices - realizable experiment or teaching aid?

At least one textbook [1] uses sequential Stern-Gerlach devices to introduce to students that the components of angular momentum are incompatible observables. Viz., the $z$-up beam from a SG device ...
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What is "spin-orbit torque?"

I am trying really hard to understand the concept of spin-orbit torque. It is a new-ish discovery in the field of spintronics and has many applications for magnetic devices. The information that has ...
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Analytical solution of two-level system driving by a sinusoidal potential beyond rotating wave approximation

A quantum mechanical two-level system driven by a constant sinusoidal external potential is very useful in varies areas of physics. Although the widely used rotating-wave approximation (RWA) is very ...
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Deriving non-relativistic potentials from QFT

Some systems, like atoms, are described well by quantum mechanics, where one just gives the Hamiltonian in the form $H=T+V$ and computes the eigenvalues and eigenvectors of this operator to figure out ...
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What are problematic issues of quantum field theory in curved spacetime, when accepting semiclassical limitation?

The question is inspired from the answer to Is a QFT in a classical curved spacetime background a self-consistent theory? (I am going to reference this link as "The Q" to avoid confusion). As far as ...
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9 votes
1 answer
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Using open system dynamics to define a quantum state

Background The density matrix of a closed quantum system with Hilbert space $\mathscr H$ evolves according to the von Neumann equation \begin{align*} i\hbar\dot\rho=[H,\rho]. \end{align*} Given a ...
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Is there supersymmetry between Dirac and Klein Gordon solutions?

Usually supersymmetry is explained at the level of the action of a quantum field theory, and there are two ways to go down from QFT to relativistic quantum mechanics: either a non-covariant way where ...
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Thermalization at quantum critical point and quantum many-body scars

Quantum scar states are a hot topic in condensed matter physics. Quantum scars are the eigenstates of a many-body system (e.g. a spin chain) that weakly violate the eigenstate thermalization ...
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8 votes
1 answer
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How would you build a device to measure $L^2$ (angular momentum squared) of a particle?

The formalism of Quantum Mechanics uses angular momentum operators such as $L_x, L_y, L_z$, and $L^2$. The quantities corresponding to $L_x, L_y, L_z$ can be measured using a Stern-Gerlach apparatus, ...
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8 votes
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Is zitterbewegung physical or not?

It appears that zitterbewegung, a frequency associated with the total energy of a particle or system, is widely considered to be an unphysical quantity (e.g., Kobakhidze et.al.), @Lubos Motl, McMillan)...
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What happens with the momentum properties of the finite-well eigenstates as the well becomes deeper and deeper?

It's a reasonably standard fact (though not nearly well-known enough) that the momentum operator in the infinite square well is a very problematic beast (as explained e.g. in this and this answers). ...
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8 votes
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Double slit - higher dimensions

The double slit experiment is a real-life manifestation of the Huygens principle. As is well-known, this principle depends on whether the number of dimensions is ever or odd; as Evans1 puts it, ...
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8 votes
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How is Mössbauer spectroscopy so resistant to thermal motion?

Mössbauer spectroscopy detects tiny shifts (on the order of $\rm{\mu eV}$ or $\rm{meV}$) in a gamma ray's energy due to the chemical environment of the nucleus. The scan consists of moving a source ...
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Quantum fields from cluster-decomposition principle

I would like help proving Weinberg's claim (I've quoted him below) that quantum fields are an unavoidable consequence of merging particle-based quantum mechanics with both Lorentz invariance and the ...
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$U(N)$ gauged quantum mechanics

I'm studying the $U(N)$ gauge theory theory in 0+1 dimensions. The aim is to show that this is equivalent to a matrix model. Is there any literature on this topic? The action I am interested in is $$...
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Can we have consistent histories inside a black hole?

A consistent history is a POVM set of observables corresponding to a time-ordered product of projection operators. For gauge theories, not any old operator will do, only gauge-invariant observables. ...
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3 answers
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How would a realist interpretation of the Mermin-Peres square look like?

How would a realist interpretation of the Mermin-Peres square with counterfactual definiteness and the existence of states prior to measurements look like?
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1 answer
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Trying to understand mixed states

I took a basic quantum chemistry course (McQuarrie's "Quantum Chemistry"), but it never dealt with mixed states -- only pure states (or if it did, we never got to it in class). So I'm trying to ...
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7 votes
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What does it mean for two variables to be canonically conjugate?

The word "canonical" has been used in many of my classes (canonical ensemble, canonical transformations, canonical conjugate variables) and I am not really sure what it means physically. ...
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7 votes
2 answers
408 views

Number of bound solutions of electronic Schrödinger equation

How can I tell how many solutions I will have for an electronic Schrödinger equation ? For example, solving it for the hydrogen atom we get infinitely many solutions \begin{equation} ...
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Is there any heat loss in chiral edge channels of topological insulators?

If we are working with nontrivial topological insulator with broken time reversal symmetry then we can expect that we have some chiral edge states. Chiral states have the property that the current can ...
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7 votes
1 answer
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Does the Schrodinger Equation yield a unique wave function and density?

I am learning DFT and the Hohenberg Kohn Theorem of Existence. And it says that there is a one-to-one correspondence between the external potential and the density. However the proofs that I have seen ...
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7 votes
0 answers
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Kraus operators for two interacting harmonic oscillators: Problem with the calculation (Ex. 8.21 of Nielsen-Chuang)

I'm working with Exercise 8.21 of the Nielsen-Chuang book on quantum information. It illustrates the amplitude-damping quantum channel by the interaction between two harmonic oscillators (the first ...
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7 votes
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170 views

Can the Dirac quantization condition be derived within Lev Vaidman's formalism without gauge fields?

Textbooks often claim that phenomena like the Aharonov-Bohm effect require that any local formulation of quantum gauge theory use gauge potential fields. (It's also sometimes claimed that the A-B ...
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7 votes
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The number of mutually-unbiased bases in dimension $d$

This recent answer points to the concept of a mutually-unbiased pair of bases, which are orthonormal bases $\{e_1,\ldots, e_d\}$ and $\{f_1,\ldots, f_d\}$ of a $d$-dimensional Hilbert space $\mathcal ...
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7 votes
0 answers
229 views

What's the physical meaning of the eigenvalues of the spin-flipped density matrix?

In the computation of the entanglement of formation(EoF) of a 2 qubits mixed state, $\rho$, according to Wooters, we need to compute the concurrence of the state by computing the eigen values $\{\...
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7 votes
1 answer
218 views

What conserved quantity causes degeneracy of spectrum in rational polygonal billiards?

Apart from Laplace-Runge-Lenz vector conservation in Coulombic and something similar in harmonic and other central potentials, something leads to existence of periodic trajectories in such systems as ...
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7 votes
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159 views

Completely positive maps and symmetric states

Let $\mathcal{N}$ be a completetely positive trace preserving map (aka a quantum channel) acting on a finite dimensional system $\mathrm{A}$, and let $\pi$ denote the maximally mixed state on $\mathrm{...
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7 votes
2 answers
893 views

Is the trajectory of a quantum particle a well defined concept and how does this depend on the interpretation of quantum mechanics?

A common statement about quantum physics is that the "trajectory" of a particle is no longer a well defined concept because of the uncertainty relations for position and momentum. If one interprets ...
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General formulation for fermions

Let us look at a set of fermionic creation and annihilation operators $b_n$, $b_n^\dagger$ with $n \in \mathbb{N}$. What is the precise relationship between this and this sequence here (partition ...
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Could energy be stored into (not extracted from) the quantum zero point field (like a battery)?

In order to explain the question clearly, I will make a short introduction. In 1962, Josephson predicted that for a sufficiently thin insulating layer, it should be possible for Cooper pairs to ...
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7 votes
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Looking for modern results in semiclassical physics and relevant references

What are some important approximations, especially those that are state-of-the-art, used to approximate the many-body dynamics of atoms and molecules in the semiclassical regime? To be clear, I'm not ...
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7 votes
1 answer
902 views

Is it possible to construct a quantum "computer" using laser light similar to the double-slit experiment?

Is it possible to construct an arrangement of optical devices (lasers, mirrors, slits, splitters) such that the construction could carry out a single quantum "computation"? I understand that such a ...
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7 votes
1 answer
231 views

Quantum Logic and Quantum Field Theory

Quantum Logic is a very interesting and powerful answer to the problem of Quantum Mechanics foundations. Nevertheless this approach is usually developed in a non-relativistic framework. Is it still ...
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7 votes
2 answers
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Why does symmetry of the system depends on the gauge for particle in magnetic field?

Consider a particle in two dimensions with an external magnetic field in the $z$-direction. The vector potential can be chosen to be $$\mathbf{A}=-By\ \hat{x}$$ so that the Hamiltonian given by $$H=\...
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6 votes
0 answers
138 views

Question about Sakurai's $SO(4)$ symmetry section

In Sakurai's Quantum mechanics book, he says the hydrogen atom has $SO(4)$ symmetry by explicitly exhibiting operators $I_i,K_i$ that satisfy the commutation relation of the Lie algebra $so(4)$. ...
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6 votes
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163 views

Using perturbation theory or small oscillation approximation in Harmonic oscillator

Let us assume, we are given the following potential, $$V(x)=\frac{1}{2}ax^2-2x+\epsilon x^3$$ We need to find the energy levels of a particle bound in this potential Let us think of the ground level ...
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6 votes
0 answers
87 views

A Venn diagram for: (non-)locality, (non-)realism, (non-)contextuality, (non-)signalling, (dis-)entanglement

I recently asked a (yet-unanswered) question about the relationship between state-dependence and violations of realism. The more I read on the subject, the more I find myself digging deeper in a ...
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6 votes
0 answers
226 views

Complete localization in 2D

The two-dimensional Anderson model is the model $$ H = T + \lambda V_\omega $$ where $T$ is nearest-neighbor hopping on $\mathbb{Z}^2$ and $V_\omega$ is a random potential. $\lambda > 0$ is the ...
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