Stack Exchange Network

Stack Exchange network consists of 174 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Visit Stack Exchange

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.

67
votes
0answers
2k views

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 ...
18
votes
0answers
502 views

Uncertainty relation for non-simultaneous observation

Heisenberg's uncertainty relation in the Robertson-Schroedinger formulation is written as, $$\sigma_A^2 \sigma_B^2 \geq \left|\frac{1}{2} \langle\{\hat A, \hat B\}\rangle -\langle \hat A\rangle\...
17
votes
0answers
4k views

What are Griffiths effects in the context of condensed matter physics?

From a cursory examination of the literature I've gathered the following: it seems that ordered systems have a "clean" critical point, at which the system makes a sharp phase transition, and that ...
15
votes
0answers
634 views

What is the largest number of bosons placed in a BEC?

What is the record for the largest number of bosons placed in a Bose-Einstein condensate? What are the prospects for how high this might get in the future? EDIT: These guys reported 20 million ...
12
votes
0answers
165 views

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 ...
12
votes
0answers
741 views

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}^\...
12
votes
0answers
290 views

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?
11
votes
0answers
104 views

Is the converse of Weinberg's statement on the cluster decomposition principle true?

In Weinberg's "The Quantum Theory of Fields, Vol. 1", Section 4.4, page 182, the author says: We now ask, what sort of Hamiltonian will yield an $S$-matrix that satisfies the cluster decomposition ...
10
votes
0answers
249 views

Two interacting electrons in infinite square potential - is there a solution?

If one were to look at Schroedinger's equation for two interacting electrons in a one dimensional infinite square well, it would something like this: $$-\frac{\hbar^2}{2m}\partial^2_{x_1}\psi(x_1,x_2)...
10
votes
0answers
252 views

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 ...
9
votes
0answers
146 views

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 ...
9
votes
0answers
137 views

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)...
9
votes
0answers
162 views

How can one recover the classical frequency-modulation Bessel sidebands from a quantum emitter in a harmonic well?

Consider an atom that emits at frequency $\omega_0$ that's located at a position $x$ that moves under the influence of a harmonic oscillator at frequency $\nu$. In both classical and quantum physics, ...
9
votes
0answers
180 views

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 ...
8
votes
0answers
129 views
+50

Why this is classical correlation and not full (classical + quantum) correlation?

Let a quantum system be given which has two subsystems $A$ and $B$ so that the Hilbert space decomposes $\mathscr{H}\simeq \mathscr{H}_A\otimes \mathscr{H}_B$. If the state of the system is $\rho$, ...
8
votes
0answers
85 views

Does the trace distance specify a unique state

In quantum information, we frequently use the trace distance (see definition) to look at how similar two states are. If I had a known complete set of states $\{\rho_i\}$ and some unknown state $\...
8
votes
0answers
162 views

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). ...
8
votes
0answers
289 views

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 ...
8
votes
0answers
493 views

Green functions and density matrix

tl;dr The single particle density matrix is directly related to NEGF as shown here, I wish to find a way to relate NEGF also to density matrices which describe probability distribution of many body ...
8
votes
0answers
339 views

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, ...
8
votes
0answers
524 views

How is conditional probability handled in quantum mechanics?

In ordinary probability theory the conditional probability/likelihood is defined in terms of the join and marginal likelihoods. Specifically, if the joint probability of two variables is $\mathcal{L}(...
8
votes
0answers
84 views

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 ...
8
votes
0answers
404 views

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 ...
8
votes
0answers
722 views

How to do time evolution of operators in the Heisenberg Picture while staying in the Heisenberg Picture

Consider the time evolution of an operator in the Heisenberg picture: $$\tag{1}i\hbar \frac{d}{d t} \hat{A}_{H}(t) = \left([ \hat{A}_S(t), \hat H_S (t)] + i\hbar \frac{d}{d t} \hat{A}_S(t) \right)_H.$...
8
votes
0answers
393 views

Is the Hilbert space spanned by both bound and continuous hydrogen atom eigenfunctions?

As e.g. Griffiths says (p. 103, Introduction to Quantum Mechanics, 2nd ed.), if a spectrum of a linear operator is continuous, the eigenfunctions are not normalizable, therefore it has no ...
8
votes
0answers
214 views

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. ...
7
votes
0answers
131 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{...
7
votes
0answers
178 views

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 ...
7
votes
0answers
173 views

Can different Floquet replicas be distinguished (within Floquet's theorem)?

According to Floquet's theorem, two quasi-energies separated by $n\hbar \omega$ represent the same state. According to this, I would think different replicas are indistinguishable experimentally. ...
7
votes
0answers
1k views

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 ...
7
votes
0answers
302 views

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 ...
7
votes
0answers
242 views

$U(N)$ 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 $$...
6
votes
0answers
315 views

Is Bohmian mechanics really incompatible with relativity?

This is something I've been wondering about. For those who don't know, Bohmian mechanics is an interpretation of quantum mechanics that is in the class of what are known as "hidden variable theories", ...
6
votes
0answers
67 views

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 ...
6
votes
0answers
113 views

What quantum measurement formalism is easiest to implement physically?

As part of my studies and research, I have learned to work with three different measurement formalism which I define to avoid any ambiguity with the nomenclature: General measurements, which are ...
6
votes
0answers
28k views

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 ...
6
votes
0answers
192 views

Free Will Theorem question

The Kochen-Specker Theorem says, if I understand it correctly, that the results of spin measurements cannot be predetermined independent of measurement. They get to this conclusion by describing 33 ...
6
votes
0answers
182 views

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 ...
6
votes
0answers
1k views

What is the Landé g factor?

What is the Landé g factor? I know that it gives the relation between magnetic moment and angular moment, but i wanted to know why are those magnitudes related to each other and why is the magnetic ...
6
votes
0answers
113 views

Known properties of a specific class of quantum states

Recently, I have been studying a quantum protocol for the "Hidden Matching" problem that makes use of states that can be expressed as $$|\psi\rangle=\frac{1}{\sqrt{n}}\sum_{i=1}^n (-1)^{x_i}|i\rangle$$...
5
votes
0answers
91 views

Why is Argon a noble gas?

Why is Argon a noble gas given that the 3d subshell is still empty? I understand that in Helium the n=1 level is full, so it is a noble gas. Now, Beryllium has a full 2s subshell but it is a metal. ...
5
votes
0answers
88 views

A question regarding Leonard Susskind's ER=EPR lecture

https://youtu.be/OBPpRqxY8Uw?t=1315 Right at this instance of the video Susskind starts talking about how space is actually connected by entanglement. (You should watch the video for a accurate ...
5
votes
0answers
79 views

What is the difference between a harmonic oscillator and a cavity mode?

this question might seem ridiculous to you, but I will really appreciate it if you could clarify the difference between a harmonic oscillator mode and a cavity mode. Below is my depiction. For a ...
5
votes
0answers
69 views

How to understand the failure of Leibniz rule in Lindblad type Heisenberg equation?

Dual to the well-known Lindblad master equation for density matrices, the equation for operators (in the sense of Heisenberg equation) is written as $$ \frac{d}{dt}\hat{A}=i[H,\; \hat{A}]+\sum_i \...
5
votes
0answers
94 views

Reference guide for standard descriptions of materials

Is there any reference that has a coherent list of materials and what type of approximate Hamiltonian to best describe them with (where it is known). Particularily I am looking for the following bits ...
5
votes
0answers
114 views

How to derive the Klein-Nishina formula from the Dirac equation?

I'm looking for the simplest demonstration of the Klein-Nishina formula, from the Dirac equation without the field described as a quantum operator: https://en.wikipedia.org/wiki/Klein%E2%80%...
5
votes
0answers
64 views

What is the high temperature molar heat capacity of $\mathrm{CO}_2$ (carbon dioxide)?

In determining the heat capacity of a substance we just count the number of quadratic degrees of freedom in the Hamiltonian, right? Using that logic, for the linear molecule $\mathrm{CO}_2$ in a ...
5
votes
0answers
196 views

Connection between quantum field and the wavefunction

The general question "What is a quantum field?" has been asked here before, but I'm looking for specific help in trying to iron out the details of my own personal interpretation and understanding. In ...
5
votes
0answers
42 views

Where can I find data about hyperfine levels of a given atom?

The NIST Atomic Spectra Database is an excellent resource for finding the energy levels of atoms and the transitions between them, and (together with the DLMF) is a good candidate for the number-one ...
5
votes
0answers
80 views

Kochen-Specker property in infinite dimensional systems

Motivation Entanglement and entanglement measures are traditionally defined in finite dimensional systems. Nowadays there are very well-known definitions of entanglement measures in quantum field ...