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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Is there a way to manually change the energy of a particle?

We have a relation, $E=h\nu$, where $\nu$ is the frequency and $E$ is the energy of any particle. If we have a function, $\psi$, that is an eigenstate of energy, the particle has a definite energy, ...
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Phase-amplitude decomposition from complex wave solution

Consider the stationary Schrodinger equation in 1D: $$ \psi''(x) + Q(x) \psi(x) = 0 \quad x \in [0, L] $$ I am specifically interested in the case where $Q(x)$ is monotonic and gives a single turning ...
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Momentum probability density from Wigner distribution

I want to prove that $|\hat{\psi}(p)|^2= \frac{1}{2\pi} \int W_\psi \mathrm{d}x $ where $W_\psi $ is the Wigner function. Starting with the definition I get ($z=-y$ and $u=x+z/2$): $$\frac{1}{2\pi}\...
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Coherent States of a Harmonic Oscillator

I have used the definitions of the annihilation and creation operators to determine the coherent state of a harmonic oscillator. I have derived the equation $$|\alpha \rangle=e^{\frac{-\alpha^{2}}{2}}\...
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Karen Barad's theory of agential realism - does it stand on solid scientific ground or is it quantum quackery? [closed]

Before you vote to close this question as off-topic, please note that while my interest in the topic lies on the metaphysical guesswork, my question here is specifically about Karen Barad's scientific ...
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Why is it always $\psi= A \sin kx + B \cos kx$ to solve a wave function?

Why is it always $\psi= A \sin kx + B \cos kx$ to solve a wave function instead of the one with $e^{ikx}$? Both are the solutions but the one with $e^{ikx}$ is seldom used.
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What is the probability of finding one spin of a doublet system as spin up

How can I calculate the probability of finding one spin of a doublet as spin up? Suppose I have the following system: $$|\psi\rangle=(|\uparrow\rangle \otimes |\downarrow\rangle + |\downarrow\rangle \...
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Momentum Operator [closed]

I have a problem to calculate equivalent operator. Consider p (momentum) and $x^2$ are classical variables. Please show me which is equivalent operator of $x^2$p? $\frac{1}{2} (\hat{x}^2\hat{p}+\hat{...
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Non-Hermitian eigenvalues from a Hermitian solver

I am using a numerical solver of large dense Hermitian matrices $H$ called ELPA. Is there a hacky way I can use it for non-Hermitian matrices $A$? Only basic matrix algebra is allowed. The best I came ...
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CNOT Gate in Pauli Basis

The CNOT gate is usually written as $|0\rangle\langle0|\otimes I + |1\rangle\langle1|\otimes X$ (with $X,Y,Z$ beign the Pauli Basis and $I$ the Identity). I have yet to stumble across the ...
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What is the capacitance of ferrodoxin molecule?

On Wikipedia it says that a ferrodoxin molecule is a biological capacitor which transfers electron to change the oxidation state of iron from $\text{Fe(II)}$ to $\text{Fe(III)}$. Now I simply want to ...
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If Mass Defect for a Stable nuclei is positive, why is its packing fraction negative?

Mass Defect = Mass (Initial : Mp + Mn) - Mass(Final : Observed) So if Mass Defect is positive, it means the nucleus is stable. But it is known ...
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Finding the time dependency of the matrix elements of the density operator [closed]

So I have been asked to do the above task but I am not sure how to do it correctly. A hamiltonian is given as: $$ -((0 A), (A, 0)) $$ $A$ being a matrix element. I decided to do: $$ p_{11} = \tfrac12 \...
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Identical particles in Bohmian quantum mechanics

Particles can be distinguished by their trajectories in Bohmian quantum mechanics and there is no natural reason for imposing symmetrization (or anti-symmetrization) of the wave function of the ...
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$[(\hat{a}^{\dagger})^2, \hat{a}] = -2\hat{a}^{\dagger}$?

I'm confused by a line in the following wikipedia article on the squeeze operator in deriving the action of the squeeze operator on Heisenberg basis, the article seems to imply that $$[(\hat{a}^{\...
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1 answer
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Discrete Spectrum vs Continuous Spectrum and Bounded, Scattering States

Apolgies in advance if this is a confusing ramble and multitude of questions, I'm not quite sure how to articulate myself. I am currently reading up on quantum mechanics and seem to have confused ...
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Incredible electron drift velocity in atomic thin layer of graphene?

Free electrons in atomic thin layers of graphene behave more like photons (Bosons) than fermions reaching incredible drift velocities and mobility which reach speeds as reported by this article in the ...
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Relation $\Delta x \Delta p \approx \hbar$. Show that the condition $\Delta p \ll p$ guarantees that the packet does not spread

Consider a wave packet that satisfies the relation $\Delta x \Delta p \approx \hbar$. Show that the condition $\Delta p \ll p$ guarantees that the packet does not spread appreciably in the time it ...
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Which neutral atom-based quantum sensor is hardest to build/operate?

I am currently going through the presentation, "Sensing with neutral atoms", by Grant Biedermann. I understand that, according to the talk, there are a large number of different sensing ...
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1 answer
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Why no acceptor energy level in pure semiconductor?

Why there is no acceptor energy level in pure semiconductor? (assume some holes are formed due to heat), While the holes created here to effectively conduct electricity , bonded electrons must ...
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2 answers
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What does it mean if the Fermi level crosses into the valence band? How about into the conduction band?

I've been working on this material to get more accustomed to Quantum Espresso, and I've gone on and performed calculations to get their band structures. Here are the band structures that I got for two ...
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Does this relativistic generalization of the Schrodinger equation make sense? [duplicate]

So I'm aware that the correct relativistic approach to quantum mechanics is through quantum fields, but I'm still interested in the question that follows. We know the Schrodinger equation in free ...
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Gell-Mann Low formula vs time independent perturbation

Consider a nonperturbed Hamiltonain $H_0$ and an eigenstate $|\Psi\rangle$ satisfying $$H_0|\Psi\rangle=E_0|\Psi\rangle.$$ Now consider the perturbed Hamiltonian $H=H_0+\lambda H_1$ and let $H_\...
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Is quantum entanglement the only true quantum phenomenon? [closed]

I once heard that in essence, the only truly unique quantum effect is, or is due to, quantum entanglement. Is that statement true? If true, how can I convince myself of it? If false, what are the ...
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1 vote
1 answer
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1D bound state for a real potential

The prof says: "for 1Dimensional bound states with a real potential, the wave function is real, up to a phase". The proof goes like this: 1D bound states are never degenerated. So $\Psi_{...
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Normal ordering of number operators $n$th power

In resources I keep seeing the normally ordered form of the number operator to the $n$th power, $${(a^\dagger a)}^n=\sum_{k=1}^n S(n,k){(a^\dagger)}^ka^k.$$ Why are we interested in the number ...
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Can someone please explain energy of electrons in Bohr's model?

Energy of and electron is $$E = \text{kinetic energy} + \text{negative of potential energy}. \tag{eq-1}$$ But energy of electron in the $n$th orbital is also $$E = -\frac{13.6}{ n^2} \tag{eq-2}$$ ...
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4 answers
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Why is angular momentum equal to mass times radius times velocity?

When momentum is mass times velocity, why is angular momentum mass times radius times velocity?
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2 answers
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Rydberg energy and Hubble constant

Although they are of different dimensions, the value of the Rydberg energy is very close to that of the Hubble constant. Rydberg energy (R): $2.179 \times 10^{-18}$ [Joule] = 13.6 [eV] Hubble ...
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Is there consensus among physicists that reality is fundamentally deterministic? [duplicate]

Does Heisenberg’s Uncertainty Principle mean that the universe cannot deterministically be predicted by observers, or does it mean that the universe is inherently indeterministic, meaning that the ...
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How the eigenvalue problem was solved?

In Gasiorowicz 3rd edition Chapter 3, I've tried to solve this problem I checked the solution's manual, When I tried to integrate it, the answer I got is $$ \psi(x)=Ce^{x^2/2\lambda} $$ Can you ...
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References to superpositions of vacua states, for SSB

I would like to read more about this subject, about having an unbroken symmetric superposition of the vaccua (minimum energy state), instead of directly chosing one, for computing SSB as my teachers ...
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Quantum measuring simulation

Hi I want to understand a concept that I been thinking about. I'm trying to simulate the energy measurement of a system (a many body quantum system to be precise), and I'm trying to simulate a quantum ...
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3 votes
2 answers
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How does $s$ subshell not have a node in the center despite the nucleus being there?

In most images of $1s$ subshell I see that there's no node shown at the center, and even the formula $n-\ell-1$ gives 0 as the answer. But, isn't the nucleus experimentally proven to be at the center? ...
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10 votes
2 answers
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Why were sparks created in Rutherford's alpha particle scattering experiment?

So I just read that when alpha particle hit the gold foil sparks were created. And these flashes were used to determine the angle of scattering. So were the sparks created because the alpha particles (...
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1 vote
0 answers
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What is an intuitive or simple proof of Gleason's theorem and how it relates to the Born rule?

What is an intuitive or simple proof of Gleason's theorem and how it relates to the Born rule? I tried to read the articles, but the proof seemed big and the kind that are unintuitive (im not ...
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1 answer
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Factorization of the wavefunction in a central Hamiltonian problem

I am trying to understand the topic of the title. If I consider a central Hamiltonian, so an Hamiltonian of the form $H=\frac{p^2}{2m}+V(r)$ what are the logical steps that lead me to the known result?...
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Why is this the exact shape of expectation values in the path integral formalism?

This question is about expressions of the form $$ \langle x_f, t_i | \hat{x}(t) | x_i, t_i \rangle = \frac{1}{N} \int_{x(t_i) = x_i}^{x(t_f) = x_f} \mathcal{D} x~x(t)e^{i S[x]}. $$ In the following ...
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Why does doping allow for Cooper pairs in high temperature superconducting cuprate compounds in Resonating Valence Bond Theory?

Preface: I'm a first years masters student (only in my second quarter) and I'm well aware that RVB theory is an extremely complex and high level topic. I have to give a presentation for one of my ...
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1 answer
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Solving Schrodinger equation with a harmonic oscillator potential

This is referenced from the textbook Introduction to Quantum Mechanics by Griffith. I am learning about the application of ladder operators to solve algebraically the Shrodinger equation for harmonic ...
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Regarding Griffith quantum mechanics problem 2.47: Square double well

I have a query regarding part b) of the question. I do not understand in particular why $E_1$ and $E_2$ will vary as a function of $b$. With my understanding of the double rectangular potential ...
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Would a quantum theory of gravity necessarily violate relativity? (quantisation of speed of light?) [closed]

The way I understand Quantum Mechanics, observables are "promoted" to operators. Relativity (General and Special) are defined around the constancy of speed of light $c$. This is the speed of ...
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Degeneracy of Photons

The density of states for a photon gas is defined by, $$D(\epsilon)=\frac{g}{2\pi^2}\frac{\epsilon^2}{(\hbar c)^2} $$ where g is the number of independent internal states for a photon. The question is ...
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1 answer
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Why $ \vec \mu$ is induced by $\vec B_{ext}$?

I have read that in the presence of an external magnetic field $\vec B_{ext}$ the magnetic moment induced on a paramagnetic ion is $\vec \mu=g \mu_B \vec J$ where $g$ is the Landé g-factor. Why is $\...
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9 votes
1 answer
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Resolution of the identity of operator with mixed spectrum

In most quantum mechanics text books, the resolution of the identity or completeness relation is stated in the following (or similar) form $$ \mathbb I_\mathcal H = \sum\limits_n |\lambda_n\rangle \...
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3 answers
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Quantum mechanics, are simultaneous eigenstates to be intended always as a tensorial product of two eigenstates?

The question is the one of the title, let $\hat{O}_1$ and $\hat{O}_2$ two commuting operators: $[\hat{O}_1,\hat{O}_2]=0$, there is an orthonormal basis formed by their simultaneous eigenstates. These ...
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1 vote
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How do massless particles have the same chirality and helicity when they are different properties?

I read this article about chirality and helicity. At some point it says For massless particles, chirality is the same as helicity. But as far as I know, helicity takes form in numbers, $(-1/2, +1/2)...
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1 vote
1 answer
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Complex Coupling Strength in Light-Matter Interaction Hamiltonian

The quantised electric field operator is given by : $$ \hat{\mathbf{E}}(\mathbf{r},t) = i\sum_{\xi}E_{\xi}\left(\mathbf{u}_{\xi}(\mathbf{r})a_{\xi}-\mathbf{u}^*(\mathbf{r})a_{\xi}^{†}\right) $$ where ...
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2 votes
1 answer
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Why does applying the kinetic energy operator to a free particle result in a divergent integral?

The wavefunction of a free particle is just $$\psi = Ae^{i(kx-\omega t)}$$ and when you plug this into the Schrodinger equation you get the dispersion relation $$E = \frac{\hbar^2 k^2}{2m}$$ However, ...
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1 answer
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System of two objects (Quantum Mechanics) [duplicate]

If we consider a system made out of two subsystems (i.e particles etc) and we do not consider interaction between the two subsystems. Then we have: $H_1=-\frac {\hbar^2}{2m_1}\Delta_1 + V(r_1)$ (...
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