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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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How does light 'choose' between wave and particle behaviour?

Light exhibits wave behaviour in phenomenon such as interference but particle behaviour in the photoelectric effect. How does light 'choose' where to be a wave and where to be a particle?
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Decomposition of the maximally entangled states

We know that the set of symmetric bipartite pure states is spanned by $S=\{|\phi\rangle^{\otimes 2},|\phi\rangle \in \mathbb{C}^d\}$. I want to know if the maximally entangled state $|\psi\rangle = \...
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Symmetry of the spin function and T0 and S states

$|T_0\rangle = \frac{1}{\sqrt{2}}(|\uparrow \downarrow\rangle + | \downarrow\uparrow\rangle )$ is a triplet state, whose spin function has to be symmetric. $|S \rangle = \frac{1}{\sqrt{2}}(|\...
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Intuition behind Bose-Einstein Condensate

I am trying to learn about Bose–Einstein (BE) condensate, and in doing so I encountered some bizarre phenomena, which is a norm in quantum mechanics. I realized matter would turn into 'waves' and lose ...
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Does time emerge from entanglement?

I stumbled upon the hypothesis that time emerges from quantum mechanics as long as the observer is part of the system. That is, the evolution of an entangled state can serve as a clock for an observer ...
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Where does the inconsistency between QM and general relativity stem from? [duplicate]

I understand special relativity works with QM (as seen by QFT) and I know that there is some discrepancy between GR and QM. Could someone elaborate on that? Where does the inconsistency stem from? ...
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Zeeman effect - accidental degeneracy for high fields?

For a low level field, the energy splittings are given by $$\Delta E(L, S, J, m_J) = \mu_B m_j g_L B_z$$ where $g_L$ is a g-factor. This predicts a separation into $(2J+1)$ levels, so completely ...
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1answer
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What is frequency entanglement?

If frequency (or energy) is regarded as a quantum property, can one generate a pair of photons with frequency entanglement? What would be the uses of this type of entangelment in say, sensing? How ...
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Why an insufficient overlap cause vanishing exchange interaction?

Why should the exchange interaction vanish if the atoms do not have sufficient overlap in their overfunctions? For exchange interaction not to vanish, the only requirement seems to be that the ...
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1answer
117 views

Bloch sphere representation of an eigenvector

I'm trying to work through a problem that wants me to determine the Bloch sphere representation of the eigenvectors of $\sigma_{z}$. I'm working in bra-ket notation so these would be $\ v_{+} = |0\...
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Three spin states of a spin-1 particle

For a spin-1 particle at rest, it has three spin states(+1, -1, 0, along the z axis). If we rotate the z axis to -z direction, the spin +1 state will become the spin -1 state. Can we transfer the spin ...
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Symmetry operators of a Bloch Hamiltonian

Consider a lattice with a 3 atom basis, e.g. the Lieb lattice, and some completely arbitrary on-site energies and hopping energies and phases between the different atoms. In momentum space we can ...
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Derivation of gradient of the expectation of local energy

Background: In Variational Monte Carlo, given a Hamiltonian $H$ and a wave function $\psi_\alpha$ dependent on some parameter(s) $\alpha$, we have defined a quantity known as the local energy, $$E_L =...
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2answers
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Why can many distinguishable particles be in the same quantum state?

In Boltzmann distribution, it says we have no restrictions on how many particles there are in a same quantum state. BUT the contradiction is: Distinguishable particles mean we think their wave ...
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1answer
242 views

Fine Structure Correction

The fine structure correction is composed of the relativistic correction and spin-orbit coupling. The lowest-order relativistic correction to the Hamiltonian is $$ H_r' = -\frac{p^4}{8m^3c^2}$$ ...
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1answer
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Time independent perturbation theoery

Why do we talk of transitions only in time dependent perturbation theory when the eigen states are corrected even in time independent perturbation theory? If we can,for sake of argument,say : eigen ...
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When can quantum states be distinguished with certainty?

Through a few examples, I'd like to learn under what circumstances can different quantum states be distinguished from each other. So for example, the standard quantum teleportation scheme starts out ...
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Why Use the Non-Relativistic Momentum Operator in Relativistic Quantum Mechanics?

In deriving the Klein Gordon equation one starts out with the relativistic energy relation $E^2 = p^2 + m^2$ and substitutes the quantum momentum operator that corresponds to non-relativistic QM, $\...
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Eigen value of a unknown system [on hold]

Why we are using operator for finding the eigen value of a unknown system
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3answers
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Encoding infinite information in a qubit vs. classical system

In this Quantum Computing article by Michael Nielsen he argues about some of the limitations imposed by quantum measurement. In particular how the amplitude $\alpha$ of a single qubit $\alpha |0> +...
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Symmetry propertis of the 3-J symbol from the symmetry properties of CG coefficient

I use the relation between 3-J symbol and the CG coefficient. But using the symmetry propertis of CG coeficient, I am not able to arrive at the symmetry properties of 3-J symbol normally used. Even ...
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0answers
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How does the collision between two atoms work?

Considering the quantum mechanical model for an atom, what exactly happens when two atoms (say, two Ca2+ ions in a Brownian motion) collide with each other? As I know, this collision is not like a ...
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1answer
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Does the wave function contain the information of the particle's mass?

It is said that wave function contains "all" the information about a particle but I don't see how I can get the mass from wave function. Further, it is able to judge what kind of particle it is by ...
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1answer
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Scalar product of free field and conjugate momentum

Given $[\Phi (x), \Pi(y)] = \delta^{3}(x-y)$,$ $ $\Phi|\phi\rangle = \phi(x)|\phi\rangle$ and $\Pi|\pi\rangle = \pi(x)|\pi\rangle$, I am trying to prove $\langle\phi|\pi\rangle \sim e^{i\int d^{3x}\...
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1answer
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Decay of a scalar Particle-Symmetry factors

Consider the Lagrangian $$\mathcal{L} = \dfrac{1}{2} (\partial_{\mu}\phi_{1})^2 + \dfrac{1}{2}(\partial_{\mu}\chi)^2 - \dfrac{M_1^2}{2}\phi_{1}^2 -\dfrac{M^2_\chi}{2} \chi^2 - \dfrac{\mu_\chi}{2} \...
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Ladder Operators - Quantum Mechanics [on hold]

In my lectures notes, we define the raising operator as $$L_+ \Phi_{l,m_l} = \hbar \sqrt{l(l+1) - m_l (m_l + 1)} \hspace{1mm} \Phi_{l, m_l + 1}$$ Then we later look at spin-orbit coupling using ...
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what is the cause of the first atom moving in moving?

I'm a computer student and I know nothing about physics and physics.stackexchange, so if I did something wrong, tell me to correct it (for example tagging). and ...
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1answer
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Can we exlain Bell's Theorem without dwelving into Quantum Mechanics?

I have recently started learning Quantum Mechanics. We learnt some things on light polarization, so I referred to this site. Luckily I stumbled upon this answer which links to this site which sated my ...
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1answer
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Matrix representation of spin-1/2 operators in Sakurai

Hello and thanks for reading. I'm an undergrad working through the first chapter of Sakurai's text and was going through the principles of the spin-1/2 system. The author demonstrates closure and ...
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1answer
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Direction of propagating wave in quantum barrier

Consider a step potential $V(x)$ where \begin{align} V(x) & = 0; \quad x\leq 0 \\ V(x) & = V_0; \quad x> 0 \end{align} Now consider the case where $E_0<V_0$. The solutions of the ...
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1answer
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Schrödinger equation variable substitution

Here is the equation sets: $$\frac{-h^2}{2m}\frac{d^2\psi}{dx^2}+\frac{h^2}{2m}\left(\frac{\rho(\rho-1)}{\sinh^2x}-\frac{\lambda(\lambda-1)}{\cosh^2x}\right)\psi=E\psi\tag{1}$$ there is a variable ...
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Einselection locality in decoherence theory

Consider two polarity-wise entangled photons A and B in an EPR experiment. The process of measuring the polarization of photon A by Alice is described by the decoherence of the 2-photons system ...
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What is the escape velocity of a neutron particle (not neutron star)

I'm not sure if this question makes sense (if not maybe you can explain why) But if the neutron has mass and have a size, then it should have a escape velocity in the "surface" right? I know the ...
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1answer
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Derive Hamilton's Principle of Stationary Action Only from Unitarity in Quantum Mechanics?

In this Question I want to give a derivation of Hamiltons Principle of Stationary action, and my question to the community would be, whether my argument is flawed. The System I want to look at is (...
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1answer
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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)...
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Integration by Parts - Calculus of variations [on hold]

I've encountered an expression while doing a QM question where we make a transformation $\Psi \to \Psi + \delta\Psi$ to the Hamiltonian. $\Psi$ is normalised, as is $\Psi+\delta\Psi$: $$\int d^3r \...
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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 ...
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Why does the Lie algebra corresponding to the unitary group contain Hermitian operators?

I saw an awesome derivation of Schrodinger's equation on Wikipedia. Part of it relies on: We also know that when $t' = t$, we must have the unitary time evolution operator $U(t, t) = 1$. Therefore, ...
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What exactly is a bound state and why does it have negative energy?

Our professor hasn't explained what bound states are. Could you give me an idea of what they mean and their importance in quantum-mechanics problems with potential (e.g. a potential described by a ...
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Why don't electron-positron collisions release infinite energy?

Questions of the form: An electron and a positron collide with E MeV of energy, what is the frequency of the photons released. quite often come up in my A Level course (for often fairly arbitrary ...
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1answer
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Probability of successive measurements

Suppose I have states $|1\rangle$ and $|2\rangle$, and my system is in a quantum mixed state \begin{equation} c \left( |1\rangle + \sqrt{3} |2\rangle \right). \end{equation} In a first measurement I ...
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1answer
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Does an antiparticle leave a different (from the normal particle) mark in a bubble chamber experiment

Experimentalists usually have experiments where they scatter particles superheated transparent liquid, thus checking for the particle's traces. These particles can be for example quarks, and ...
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Neutron decay discrepancy

I have been reading the article Neutron Lifetime Puzzle Deepens, but No Dark Matter Seen on the present methods of measuring the life span of neutrons The bottle method measures a mean lifespan which ...
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1answer
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Choosing approximate eigenfunctions

In the variational approach of estimating the ground state energy of a system we choose an approximate eigenfunction dependent on certain parameters and then minimize the expectation value of the ...
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2answers
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Orbital angular momentum quantum numbers - subtracted?

Reading Griffiths' Quantum Mechanics. We have the electronic confirmation of Carbon as $$(1s)^2 (2s)^2 (2p)^2$$ in the ground state. He says There are two electrons with orbital angular ...
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Expectation value of $x,y,z$ for general $nlm$ state of hydrogen atom

How to calculate expectation value of $\langle x\rangle, \langle y\rangle,\langle z\rangle$ for the general $\psi_{nlm}$ state? $x$ has $\sin(\theta)\cos(\phi)$ angular part which can be expressed as $...
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2answers
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How to estimate the temperature required for the 2nd energy level of hydrogen to be occupied?

In my atstrophysics lecture today we were covering atomic spectra and we saw that at both the hot and cool end, the atomic spectra of stars showed a very weak balmer series. The reason being at the ...
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1answer
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What would happen if the opposite complementary variables of two entangled particles were measured at the same time?

Many explanations about the uncertainty principle and its related EPR paradox state that it is impossible to measure opposite complementary variables on different entangled particles; for example, ...
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Is there any relation between spin and gravity?

Is there any relation between quantum spin and gravity? Are there experiments that show or motivate that there is or isn't a relation between the two?
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Spin precession for Rabi oscillations : interpretation with magnetic field in rotating frame

The model considered Consider an atom modeled by a two level system of energy $\hbar \omega$. We assume this atom is interacting with an electric field through electric-dipole interaction. The full ...