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.
6,249
questions with no upvoted or accepted answers
5
votes
0
answers
622
views
Particle in a box as a quantum field
A common introductory quantum system is the single particle in a 1 dimensional square "box" or well with infinite potential walls.
Is there a reasonably introductory treatment of this system in the ...
- 459
5
votes
0
answers
507
views
Franck-Hertz experiment - the shape of the I/V relation graph
Why does the I/V graph of Frank-Hertz experiment looks like a spindle? I understand the reson of the periodic structure but don't understand why the maxim of the current goes with a gradually flat ...
- 121
5
votes
1
answer
287
views
Transitionless quantum driving for specific eigenstates
Transitionless quantum driving is a concept that was invented by Berry in 2009.
In his article on transitionless quantum driving he showed that it is possible to speed up adiabatic evolution of ...
- 1,095
5
votes
1
answer
536
views
Understanding the Plasmon dispersion relation to first approximation
Plasmons are quantized oscillations of the charge density in solids, and are found in basically all conducting materials in nature.
For light in vacuum, the dispersion relation is required for ...
- 7,823
5
votes
0
answers
224
views
Clarification about Heisenberg’s 1925 paper and the Bohr-Sommerfeld rule
I am reading Heisenberg's 1925 paper and there is one point that I feel is crucial yet not explained well enough.
After he establishes $x(t)$ as a matrix, calculates $x(t)^{2}$, and talks about non-...
- 8,346
5
votes
0
answers
495
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 ...
- 602
5
votes
0
answers
2k
views
From the Heisenberg-Langevin equation to the Lindblad equation
In an open quantum system, one can easily derive the Heisenberg-Langevin equation of motion which describes the time evolution of creation/annihilation operators (e.g., in a cavity)
$$\dot{a}(t) = i[H,...
- 151
5
votes
0
answers
379
views
Measurement in the context of unitary evolution
My text describes how "projective measurements together with unitary dynamics are sufficient to implement a general measurement" and goes on (pp. 94-95) to demonstrate why this is so, but there are ...
- 5,087
5
votes
0
answers
640
views
Intuitive understanding in QFT
I recently read a bit about the Schrodinger picture in QFT and wavefunctionals, see e.g. Polchinski's String Theory lectures, and I wanted to ask if the intuitive understanding of QFT I got is "right"...
- 281
5
votes
0
answers
2k
views
Relation between Kraus operators and the Choi matrix
Let $\Phi$ be a CPTP map on density operators for a fixed $n-$dimensional state space and fix a basis $\{ | j\rangle \}$. I'm trying to understand the relationship between the Choi matrix $$M_\Phi:= \...
user138458
5
votes
2
answers
2k
views
Polarization of light and transitions in a Magneto Optical Trap
After reading this question, I realized that I didn't really understand how a MOT works in detail. I was always relying on the simplistic picture given in textbooks which never addresses the actual ...
- 163
5
votes
0
answers
143
views
Is this short paper correct?: "Heating the coffee by looking at it. Or why quantum measurements are physical processes"
I've just found the following paper in arXiv written by a Spanish politician who is also a physicist. In it he claims that you can setup a sequential Stern-Gerlach-type experiment in such a way that ...
- 51
5
votes
0
answers
148
views
A question about the emergence of 'spin' from relativistic QM
I know that quantum-spin is not equivalent to the spinning of a classical object about an axis passing through it, although there are some similarities.
I also know that spin naturally emerges out of ...
- 1,713
5
votes
0
answers
736
views
The ground state of arbitrary Potential Function
How can one say that the number of nodes in the ground state must be nodeless . And how one can ensure that, when one gets up in the energy spectrum, for consecutive States the difference of number of ...
- 978
5
votes
0
answers
124
views
Would a pseudo-random seed qualify as local hidden variable in Bell's Theorem?
I am currently trying to understand Bell's Theorem in Quantum Mechanics, and I have been wondering if the following interpretation would fall under the local realism / hidden variables.
Consider an ...
- 151
5
votes
1
answer
397
views
Energy in dynamical variational principle
In quantum mechanics we use variational principle in order to find approximate expression for the ground state. Lets assume our probe wavefunction $|\Psi\rangle$ can be expanded in orthonormal basis
$...
- 2,070
5
votes
0
answers
1k
views
Spin 1/2 wavefunction transformation under inversion and mirror symmetry
I'm considering group-theory applications to condensed matter physics now. In particular I work with the following paper: http://journals.aps.org/pr/pdf/10.1103/PhysRev.100.580 and try to understand ...
- 471
5
votes
0
answers
327
views
Is there a proof that the number of eigenstates is countable for a bound system?
When you solve Schrödinger equation for a free particle with no boundary conditions your eigen states are indexed by quantum number $k \in \mathbb R $ and $\mathbb R$ isn't countable but if you add a ...
- 1,414
5
votes
1
answer
327
views
Doppler-shift of AC-electricity
A tram is powered by overhead wire, the wire has alternating voltage of 1000 V RMS, the frequency of the alternating voltage is 50 Hz. The rails are the other wire.
The tram is moving at speed 100 m/...
- 1,978
5
votes
0
answers
238
views
MRI and precession
A lot of explanations of the quantum mechanics of MRI discuss the precession of a proton in an external magnetic field, for example here:
http://www.physicscentral.com/explore/action/mri.cfm
Doing ...
- 1,209
5
votes
0
answers
213
views
Geometric measure of entanglement for fermions or bosons?
For a system consisting of multiple components, say, a spin chain consisting of $N\geq 3 $ spins, people sometimes use the so-called geometric measure of entanglement. It is related to the inner ...
- 1,179
5
votes
0
answers
246
views
Why does this 'Quantum Pinned' superconductor allow easy repositioning
I'm confused by videos such as this (popular demonstration of 'Quantum Levitation'):
https://www.youtube.com/watch?v=Ws6AAhTw7RA
So my current understanding of superconductors is that when in the ...
- 151
5
votes
0
answers
292
views
Black body simulation
Black body radiation is typically understood from Planck's argument of light resonance in a box, from which the density of states is computed. Now, suppose I want to simulate a black body ...
- 336
5
votes
0
answers
356
views
A problem with the Gamow state
Consider a form of potential $U(r)$ as follows
$$
U(r)=\begin{cases}0 & 0<r\leq a \\ U_0 & a<r\leq b \\ 0 &r>b\end{cases}
$$
In this problem $r$ is the distance from the origin, $...
- 6,826
5
votes
0
answers
1k
views
Cubic perturbation to coupled quantum harmonic oscillators
I recently came across this two-dimensional problem of a particle in a potential of the form
$$V = \displaystyle{\frac{1}{2}m \omega^2} \big(y^2 + x^2y \big) - \alpha y,$$
where $x$ and $y$ are known ...
- 51
5
votes
0
answers
235
views
References to Mechanics (Classical, Quantum, Statistical) using Time-Scale calculus?
Time-Scale Calculus, is a theory which unifies ordinary (plus fractional and q-) calculus with discrete (and finite differences) calculus.
In a sense, in a similar way the Lebesgue integral (or ...
5
votes
0
answers
170
views
Local unitary transformation that maximizes overlap
Could anyone point me in the right direction (reference to papers would suffice) regarding the following:
Given two quantum states $|\psi\rangle ,|\phi\rangle \in (\mathbb{C}^d)^{\otimes n}$, where ...
- 51
5
votes
0
answers
147
views
How to distinguish Bose glass and superfluid phases in a harmonic trap?
In mean-field study of Bose-Hubbard model in an optical lattice, what parameter can be calculated to distinguish Bose glass and superfluid in a harmonic trap?
- 2,469
5
votes
0
answers
1k
views
What is a Nicolai map?
I couldn't find the definition of a Nicolai map.
What is it and what is a simple example which helps understanding it?
- 8,443
5
votes
0
answers
175
views
On an Uncertainty Relation for Angular Variables
I'm looking for a proof of the Angular Momentum - Angle uncertainty relation $$\frac{\Delta L \Delta \theta}{1-(3/\pi^2)\Delta \theta^2} \geq \frac{\hbar}{2}$$
which does not involve solving the ...
user17116
5
votes
0
answers
305
views
What is meant by "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, Bob ...
- 1,029
5
votes
0
answers
186
views
BEC in a rotating disc
Goodmorning everybody,
I have to run a numerical simulation of a Bose-Einstein condensate on a rotating disc. Now, my problem is that I became suspicious about the equation I'm using, since the final ...
- 151
5
votes
0
answers
1k
views
projective measurement & POVM
Let us consider the following completely positive map $\mathcal{B}(\mathbb{C}^n)\ni\rho\mapsto L\rho L^\dagger$, where $L\in\mathcal{B}(\mathbb{C}^n)$ is any arbitrary operator (and can have rank $>...
- 1,029
5
votes
0
answers
525
views
What is the relationship between consistent histories and path integrals?
As can for example be learned from chapter I.2 of Anthony Zee's Quantum field theory in a nutshell, path integrals can be used to to calculate the amplitude for a system to transition from one state ...
- 9,503
5
votes
0
answers
312
views
What happens to a Luttinger liquid under time reversal?
Suppose you a have an ordinary Luttinger liquid with
$$ H = \int dx \sum _{\eta= \pm 1 , \sigma =\uparrow,\downarrow } \psi^\dagger_{\eta, \sigma} (x) (-i v \eta \partial _x) \psi _{\eta,\sigma} (x). ...
user4696
5
votes
0
answers
3k
views
Energy Levels of 3D Isotropic Harmonic Oscillator (Nuclear Shell Model)
One simple way of detailing the very basic structure of the nuclear shell model involves placing the nucleons in a 3D isotropic oscillator. It's easy to show that the energy eigenvalues are $E = \...
- 238
5
votes
1
answer
678
views
Published claimed falsifications of objective collapse theories
My main source of information about objective collapse theories is this review article by Bassi et al. There seem to be some problems with the theory that its practitioners readily admit to, such as ...
5
votes
1
answer
147
views
Is a state with no fluctuations in particle density necessarily a stationary state of the Hamiltonian?
Consider a system of identical particles (bosons or fermions) with field operator $\hat{\psi}(x)$. The particle density operator is $\hat{\psi}^\dagger(x)\hat{\psi}(x)$.
Suppose that the particle ...
- 593
5
votes
1
answer
572
views
What is the maximum number of bounces a ball can be expected to make on another fixed ball of same radius on the ground?
In the book 'Quantum Mechanics' by Leonard I. Schiff, this question can be found at the end of chapter one. More specifically it asks:
A perfectly elastic ping pong ball is dropped in vacuum from a ...
- 466
5
votes
1
answer
167
views
Quantum flux tubes possible shapes
If given energy, can flux tubes be any shape as long as all quarks are connected and the amount of energy is insufficient to form a quark-antiquark pair, or will the shape of the flux tubes be a ...
- 336
5
votes
1
answer
301
views
Why do electrons in an atom only occupy stationary states, without superposition?
In simple quantum mechanical problems such as the infinite square well, we solve the Time Independent Schrodinger's equation by separation of variable, effectively getting the energy eigenstates of ...
- 244
4
votes
0
answers
110
views
Uncertainty principle for incompatible observables whose probability distributions lack well-defined moments
The Heisenberg uncertainty principle states that the product of standard deviations (or variances) for incompatible observables has a non-zero lower bound (with a zero lower bound reserved for ...
- 342
4
votes
0
answers
133
views
Schmidt decomposition of density matrix
For a bipartite system:
$\mathcal{H}=\mathcal{H}_{a}\otimes\mathcal{H}_{b}$ described by a density operator $\hat{\rho}_{ab}$, I can promote it to a vector in the Liouville space, $|\hat{\rho}_{ab}\...
- 95
4
votes
2
answers
149
views
Wheeler’s delayed choice experiment — why can’t a photon select state multiple times?
I have a question regarding https://en.wikipedia.org/wiki/Wheeler%27s_delayed-choice_experiment. I am interested in knowing why quantum mechanics seems to be so fixated in thinking that photons in a ...
- 41
4
votes
0
answers
91
views
On sum of amplitudes in Wave Mechanics
Consider Schroedinger equation, which I write in the form $$ (\mathscr{L}+V)\psi=0$$where $\mathscr{L}$ is the kinetic and time-derivative operator. Now, imagine I have two point sources 1,2 with ...
- 1,694
4
votes
0
answers
82
views
Properties of Bloch wavefunctions
I am reading the paper "Some analytical results for the resistively shunted Josephson junction" by M.J. Renne & D. Polder (PDF is available here). The cornerstone of the research ...
- 2,654
4
votes
0
answers
77
views
Question about spin-$½$ particles
Spin-½ particles needs to rotate 720º to return to its original state. If you rotate it 360º, its state will become opposite, for example $\left| ↑ \right>$ to $-\left| ↑ \right>$. This is my ...
- 41
4
votes
3
answers
161
views
Do photons and electrons of the same momentum diffract/interfere identically in same 2-slit experimental setup?
If photons and electrons of the same momentum are sent, at separate times (e.g. first photons, then electrons), through a given experimental apparatus designed to show 2-slit diffraction/interference, ...
- 97
4
votes
0
answers
116
views
Understanding the Relationship Between Stochastic Reconfiguration and Natural Gradient in Variational Monte Carlo
I've been delving into variational Monte Carlo methods, particularly in the context of ground state energy minimization for quantum wave function ansatzes. In my studies, I've come across multiple ...
- 103
4
votes
0
answers
1k
views
What is altermagnetism?
Since 2022, I have come across several papers on Altermagnetism, a novel phase of matter that breaks time reversal, but without a net magnetization. It also has many other interesting properties.
What ...
- 3,130