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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Complexity of Ab Initio quantum computation of bulk properties [closed]
Background
I'm an undergrad studying Computer Engineering, however I switched from ChemE.
I just completed Physics 2, however I've a cursory understanding of higher level Physics concepts (Hamilton ...
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How to rigorously argue that the superposition state is unstable in spontaneously symmetry breaking case
In quantum mechanics, the definition of symmetry breaking is nontrivial. See What is spontaneous symmetry breaking in QUANTUM systems?
Let me briefly summarize that question:
In spin-$1/2$ quantum ...
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Two electros in one harmonic oscillator
Suppose a one dimensional harmonic oscillator with two spin $\frac{1}{2}$ fermions. The state of each fermion can be $|n\rangle|\pm\rangle$ with $n\in\{0,1,2,\dots\}$.
My question is: which states ...
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Why does the infinite square well potential have different solutions if your boundary is $[0,a]$ vs $[-a/2,a/2]$? [closed]
I'm reviewing the infinite square well potential, and realized that if my boundaries are $[0,a]$ the constraint that $f(0) = f(a) = 0$ means that the coefficient for the $\cos$ term must equal zero. ...
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What are the strongest objections to be made against decoherence as an explanation of "collapse?"
When we measure an observable A of a quantum system, we get an eigenvalue of A. Without worrying about connotations of Copenhagen vs. MWI, etc., let's just call this "collapse."
Question: Among ...
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Negative energy eigenvalues?
If we have a free particle with a wave function consisting of a sine wave/exponential wave moving in the negative-x direction, its wave function will be:
$$|\psi\rangle=Ae^{i(kx+\omega t)}$$
The ...
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Second variation of a functional
I am trying to find the second variation of the Hartree energy functional $E_{H} [\rho]$:
$$
\dfrac {\delta^2 E_{H}}{\delta \rho (r)\delta \rho (r')}=\dfrac {\delta^2}{\delta \rho (r)\delta \rho (r')}\...
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Finding the ground state $L$ and $S$ quantum numbers of an atom
In an example in class we were asked to determine the ground state total orbital angular moment and total spin angular momentum quantum numbers $\textbf{L}$ and $\textbf{S}$ of Nitrogen with electron ...
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What do the regions of no Bell violation represent?
We often see the statements that a violation of Bell inequality means that the system shows quantum behavior or that a Local hidden variable theoretic description is not possible. One also finds that, ...
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Where are the infinite-dimensional spaces of Quantum Mechanics?
There are two questions here:
One of the confusing points about String Theory is the existence of extra dimensions. These are explained by saying that the these extra dimensions are compactified.
...
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What is the relation between entropy and quantum information? [closed]
I know that there is an important connection between quantum information and entropy, but exactly is the relation between them?
Also, is there a connection between black hole lost information and ...
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What is the radial quantum number $n_r$?
As we know, the principal quantum number $ n=1,2,3,... $ is related to the radial quantum number $ n_r=0,1,2,... $ by $$ n=n_r+\ell+1 .$$
What is the physical (or chemical) definition of the ...
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Electrons in the nuclei
Is it possible that electrons would switch place with the protons in the atom? So that the electrons in the nuclei and the protons hover around them.
Is it even possible? And why?
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Energy levels splitting in double-well potentials
As it is well known, the tunnel splitting (which are certain differences between energy levels) is the characteristic of the energy spectrum for the double-well potentials. When we calculate the ...
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What exactly is Excitonium matter?
After 50 years of theories and thwarted attempts, scientists have finally proved the existence of a new form of matter. The never-before-detected condensate is called excitonium, a name first coined ...
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Operator in quantum mechanics
I'm really confused by the definition and uses of operators in quantum mechanics. Usually we say that the state of a system is described by some vector $\lvert\psi\rangle$ in a Hilbert space $H$, and ...
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Microscopic origin of U(1) symmetry breaking in condensed matter
As far as I understand classical symmetry breaking occurs because of the inadequacy of the ensemble to account for the true thermodynamics of the system.
Consider a simple classical Ising model:
$$
H ...
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Testing Quantum Mechanics with Quantum Computing: beyond? [closed]
Quantum computing ONLY allows for unitary operations. At least in theory, as far as I know.
Could we use Quantum Computing to test the limits of Quantum Mechanics or explore the emergence of quantum ...
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Cascaded Polarizers Problem
I am going through the MIT OCW course on Quantum Physics and while looking at the recitations slide on polarizers I got stuck on the problem given in the second last slide (the extra-credit problem):
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Meaning of wave function which is in inside of the potential wall? [duplicate]
In particle in square potential barrier problem, we can easily find that some probabilities exist which express how many particles can go beyond of the potential wall.
So my question is that, can we ...
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How does Pauli's Exclusion Principle come into play for two (non-entangled) localized, free, non-interacting fermions approaching each other?
If two non-entangled free fermions with the same spatial wavefunctions (which do not yet overlap) throughout time approach each other, at what point during the overlapping of the two spatial ...
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Quantum State Representation with Commuting Operators
Let $[A,B]=0$. Then, we can find a set of eigenvectors $\{|a_n,b_n\rangle\}$ common to both $A$ and $B$. According to this, and my own understanding, it makes sense to write an arbitrary quantum state ...
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How can we certify that the randomness in the measurement outcomes is not due to randomness in the state preparation?
According to the theory of quantum mechanics, if a spin state is prepared along axis "x", and then measured along axis "z", then the result of the spin projection is probabilistic: half of the times ...
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Clifford Algebra: Wedge product, cross product, and Hodge duality
I've been reading some papers related to Bell's Theorem which involve Clifford Algebra. I am investigating it for an undergrad project but none of my professors seem to know anything about Clifford ...
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Not all self-adjoint operators are observables?
The WP article on the density matrix has this remark:
It is now generally accepted that the description of quantum mechanics in which all self-adjoint operators represent observables is untenable.[...
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How do I explain why electron energy levels are different distances apart?
I have to try and explain why the energy levels of an electron are difference distances apart. Here is the reasoning I've come up with so far;
We know that electrons themselves can actually ...
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Boson on a Torus: mode expansion
A lot of books are concerned with CFT on a torus (Euclidean signature), for instance in Polchinski's String Theory volume 1, the propagator of a free massless boson on a torus is
$$
G(z,\bar{z};w,\...
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How do environment effects enhance quantum efficiency?
In a quantum system coupled with a wet environment, such as in photosynthesis (and here), how can one intuitively explain that the decoherence gives a positive effect to the efficiency? Is it ...
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Can two distinct quantum universes ever have the same configuration, and what does it mean for many-worlds? [closed]
First, I hear that, on a whiteboard, one may casually invert causality and run time in reverse.
Next, I hear that there are interpretations of QM, like Chaitin's Great Programmer interpretation or de ...
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Does an infinite spin chain with infinitely many pure states exist?
Let ($\rho_n)_n$ be a sequence such that $\rho_n$ is a state on $\bigotimes_{n}\mathbb{C}^{2} = (\bigotimes_{n-1}\mathbb{C}^{2}) \otimes \mathbb{C}^{2}$ and for all $n$, we have that: $\rho_{n-1} =$ ...
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Question about a sentence on Griffiths QM book about the free electron gas
In line six and page 220 of the book (http://boltz.ccne.ufsm.br/pub/rsauer/estmat/2017/griffiths.pdf), it is stated that ''each intersection point represents a distinct (one-particle) stationary state'...
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What's the physical meaning of the kernel of density matrix?
The kernel of this linear map is the set of solutions to the equation A x = 0, where 0 is understood as the zero vector.
But what's the physical meaning of the kernel of density matrix?
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Maximum Uncertainty of a Measurement?
I know the state of a system at a time T1, and perform a measurement at a later time T2. My question is this: is there a maximum uncertainty on what state I could expect to measure the system?
Of ...
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What's the geometric (or representation independent) definition of central charge of Lie algebra $\mathfrak{g}$?
There is a common way described in Weinberg's Quantum Field Theory Vol.1 (P83) for introducing the concept of the central charge which I find difficult to grasp. This method uses a unitary projective ...
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How is the relation betwoon top quark and dark matter? [closed]
Is there any connection between dark matter and top quark.
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Why don't we see macroscopic "electron waves"?
A classical electromagnetic wave is, according to quantum electrodynamics, an ensemble consisting of a large number of photons, which are the minimum excitation of the electromagnetic field for a ...
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Standard deviation of the postion and momentum for the coherent state of an harmonic oscilator [closed]
Consider a particle of mass $m$ under an harmonic potential, $V=\frac12 kx^2$.
The coherence states
$$\psi_\alpha=e^{-{{1}\over{2}}|\alpha|^2}\sum_{n=0}^\infty{{\alpha^n}\over{\sqrt{n!}}}\psi_n$$
...
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Meaning of a remark by Heisenberg: Die "Bahn" entsteht erst dadurch, dass wir sie beobachten
In a paper by Joos and Zeh, Z Phys B 59 (1985) 223, they say:
This 'coming into being of classical properties' appears related to what Heisenberg may have meant by his famous remark [7]: 'Die "Bahn"...
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Valid Bogoliubov transformation?
Is it possible to diagonalize the Hamiltonian:
$H=c_1 c_2^\dagger+c_2 c_1^\dagger +\delta(c_1c_2+c_2^\dagger c_1^\dagger ) $ using the Bogoliubov canonical transformation, where the $c_1,c_2$ are ...
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Young's double slit experiment - homemade
I want to do the double slit experiment to demonstrate the particle-wave-duality to people outside of physics.
I can do it on paper and try to explain the maths and physics behind it, but it is a dull ...
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Is the Moyal-Liouville equation $\frac{\partial \rho}{\partial t}= \frac{1}{i\hbar} [H\stackrel{\star}{,}\rho]$ used in applications?
This answer by Qmechanic shows that the classical Liouville equation can be extended to quantum mechanics by the use of Moyal star products, where it takes the form
$$
\frac{\partial \rho}{\partial t}~...
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How should one think about the concept of an eigenfunction in quantum mechanics?
I was working through some problems today and came across this one:
Consider a particle in an infinitely deep potential 'well'. That is to say: $V(x) = 0$ for $-a/2<x<a/2$ and $V(x)=\infty$ ...
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How does the displacement operator act on number states $|n\rangle$?
The displacement operator generates the coherent state out of the vacuum.
$$\hat D(\alpha)|0\rangle = |\alpha\rangle$$
but I am wondering what the meaning of a displacement operator acting upon a ...
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Form of Schrödinger equation for the probability density
Is it possible to formulate the Schrödinger equation (SE) in terms of a differential equation involving only the probability density instead of the wave function? If not, why not?
We can take the ...
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Is Wigner D matrix also a spherical tensor?
Can one think of Wigner D-matrix $\mathcal D_{mm''}^{(l)}$
as a spherical tensor even in case when $m''\neq0$ ?
In other words does relation like
\begin{equation}
\tag{1}
\mathcal D^\dagger(R_1)...
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Operation on Complex conjugate
Why do we sandwich operators in quantum mechanics in such a way that the operator acts on the wavefunction and not on its complex conjugate?
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Integral of two Wigner d-functions
I want to integrate two general Wigner d-functions
$d_{k q}^{\ell}(\theta)$.
There is a simple integral in case magnetic numbers $(q,k)$ are the same:
$$ \int_0^\pi d\theta~\sin \theta ~d_{kq}^{\ell}...
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Time is defined operationally to be that which is measured by clocks
A light clock is a mechanism that produces (and counts) equal time intervals.
Yes, but, do we understand correctly what the light clock is showing?
Since we don't know what the time exactly is, we ...
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Photons and information
i just study in year 10 and might not have enough knowledge about these stuff. But what i studied in physics is a photon hits a surface and is reflected to our eyes and see what photon is reflected ...
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The potential $-x^4$ is non-hermitian?
I am currently reading a paper by Carl Bender about non-hermitian Hamiltonians. In this paper he says that $$H=p^2-x^4$$ was a non-hermitian Hamiltonian whereas $$H=p^2+x^4$$ was hermitian. It is ...
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