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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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Does QM preclude well-defined conformal structure on spacetime?

My question is whether GR and QM are incompatible in a specific and severe way. GR relates the local curvature of spacetime to the local presence of matter, but QM entails that there may be no answer ...
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Arriving at the Quantum Mechanial Potential From The Energy Eigenvalues [duplicate]

In Quantum Mechanics, we know that given a potential we can solve the eigen value problem to find out the energy eigen values and eigen functions. Now suppose in an experiment we have information only ...
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Quantum walk and the Hamiltonian operator

The Hamiltonian operator is defined on the graph $G$ as $H_{A}(t) = \exp(itA)$ where $A$ is the adjacency matrix of the graph $G$. It is said that this operator is a transition matrix and represents ...
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Numerical exact diagonalization of tight binding Hamiltonian

I want to exactly diagonalize the following Hamiltonian for $10$ number of sites and $4$ number of spinless fermions $$H = -t\sum_i^{L-1} \big[c_i^\dagger c_{i+1} - c_i c_{i+1}^\dagger\big] + V\sum_i^{...
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39 views

photoelectric effect wrt quantization [on hold]

Recently I got interested in the photoelectric effect and a little bit of quantum physics. So I have a couple of questions I'm really not in the clear about from the information I can find. When I ...
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Probability of measuring Energy [closed]

I have done the first part of the question, but in (b) and (c) are struggling me . I second part : My tutor wrote : $$ P(req.) = \frac{|\int \phi_E^*(x)*\psi(x,t) dx |^2}{|\int\: \psi^*(x,t)*\...
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Creation operator acting on a coherent state. Occupation number operator

For a coherent state $$|\alpha\rangle=e^{-\frac{|\alpha|^{2}}{2}}\sum_{n=0}^{\infty}\frac{\alpha^{n}(a^{\dagger})^n}{n!}|0\rangle$$ I want to find a simplified expression for $a^{\dagger}|\alpha\...
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24 views

Photon qubits - does photon entanglement hold for detecting polarizations?

Suppose we produce two entangled photons with perpendicular polarizations. If we place a polarizer followed by a detector for the direction of the one photon, and that detector some instant of time "...
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How does binding energy change as more fermions interact?

The subject is few-body quantum mechanics. Given a system of $N$ identical fermions (spin 1/2) interacting through pairwise potentials $V_{ij}$, how does the binding energy change between $N$ and $N+1$...
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Rigorous Treatment of Quantum Tensor Operators

Recently, my classes have introduced me to the idea of spherical tensors and the Wigner-Eckart (WE) Theorem, but my previous classes on tensors had emphasis on things like covariance, contravariance, ...
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What is the relation between chemical potential and the number of particles?

Chemical potential is defined as the change in energy due to change in the number of particles in a system. Let we have a system which is defined by the following Hamiltonian: $$H = -t \sum_i^L c_i^\...
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Measurement formalisms - POVM formalism vs Hermitian observables

I am thinking in following way of thinking about measurements in quantum mechanics. Please correct any false statements I may be making below. We start with POVMs. Let our POVM be a set of positive ...
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Why doesn't observing a photon collapse it's wave function into a B or W3 boson?

According to electroweak theory, the photon ($\gamma^0$) and weak bosons ($W^+, W^-, Z^0$) are all linear combinations or superpositions of the weak hypercharge boson ($B$) and the weak isospin bosons ...
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Operator for change of state?

I am trying to model a quantum system that has only three different classical states, so that the Hilbert space is simply $\mathbb C^3$, and let's call its standard basis $e_1,e_2,e_3$, with each of ...
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Doubt on Sakurai's proof of Wigner-Eckart theorem

In Sakurai's and Napolitano's book "Modern quantum mechanics" there's a nice proof of the theorem. This can be found also almost identical on Wikipedia's Wigner–Eckart theorem - Proof. The thing that ...
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reduced density matrix of state

given a multi particle state I have to calculate the reduced density matrix where I trace out the third particle for this I first calculate the corresponding 2D density matrix with the bra vector of ...
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Is the mass of a particle determined by the extent to which it interacts with other particles? [closed]

This is more a question about the Higgs field than anything else. If you were to take, for example, a neutrino and send it out into empty space how could you determine that it has a mass in the first ...
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Momentum uncertainty for a free particle [closed]

Free particle is in state psi k, where k is the wavenumber. Now i am trying to findout uncertainty in its momentum. I know that for free particle position is uncertain (delta x approaches to infinity) ...
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Why we don't need to normalize the scattering states?

I am new to QM, have find some wavefunction in different potentials, but there we need to normalize the wave function, for a reason that - particle should be found somewhere . So a wave-function, to ...
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39 views

Quantum Optics: entropy doesn't change!

I'm reading a paper and without any justification, the author said: Consider a single-mode cavity field initially prepared in a coherent state $|\alpha_0 \rangle$. It leaks out of the cavity through ...
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1answer
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How to use tensors and operators

I have some problem understanding how to use tensors. Let's say in Quantum Optics if I have the state in mode $b$ (where I can have two possible modes $a$ and $b$) $$|1_b\rangle = |0_a\rangle \otimes|...
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Can quantum randomness be somehow explained by classical uncertainty? [closed]

In quantum mechanics, the outcome of each measurement is random, distributed according to the squared amplitude of the wave function obtained from the Schrodinger's equation. Now, can someone suggest ...
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How unique is the Schmidt decomposition?

I read the Schmidt basis is unique "up to a phase" or as stated here in answer given by Norbert Schuch "modulo degeneracies". If I choose a Bell state $|\psi\rangle = \frac{1}{\sqrt{2}}\left(|0\...
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1answer
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What does the photon feel when it hits an asteroid on its path to earth [duplicate]

If a photon was approaching earth, after 1 minute(from earths reference frame) an asteroid comes on the photons path. And it hits the asteroid, but from the photons reference frame time doesn't pass ...
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Continuity of wave function derivative

A particle is defined by a wave function, $Be^{-2x}$ for $x<0$ and $Ce^{4x}$ for $x>0$. For the wave function to be continuous at $x=0$, $B=C$. A wave function must be continuous for it to be ...
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Some questions on coherent states and corresponding Hilbert spaces. Reproducing kernal

I have a few questions related to coherent states. I use this source https://homepage.univie.ac.at/reinhold.bertlmann/pdfs/T2_Skript_Ch_5.pdf. Using standart inner product $\langle\cdot|\cdot\rangle$ ...
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Can Quantum Mechanical Potential have a Probability Distribution

I am currently in my second semester of undergraduate quantum mechanics. We have recently starting discussing two particle systems, usually in relation to spin interactions. In all of our calculations,...
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132 views

Why is physics taught as if measurement doesn't affect the thing being measured? [closed]

I've recently started my journey in understanding the math of quantum mechanics and I've noticed a strange pattern. (I'm not saying that the popular interpretation of quantum physics is wrong or ...
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Constructing a staggered translation operator

Consider a matrix as a function of position $x$ $$C=\begin{bmatrix} 0 & A(x) \\ B(x) & 0 \end{bmatrix} .$$ Is it possible to construct a matrix $S$ that translates $A$ and $B$ oppositely? $$...
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1answer
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Confusion of measuring two quantities on a quantum system

Let's say there are two observables corresponding to two operators A and B, and let's say my system is in a state Phi where with probability 1 if I measure A I get 3 (let's say 3 Joules), If I ...
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Understanding the calculation of expectation value

The expectation value (in sense of discrete probability) can be thought of as $$ \left<a\right>=\frac{1}{N}\sum\limits^{N}{Â }\psi $$ where $N$ is the number of experiments. As the number of ...
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Rotating wave approximation : Why do we need both weak coupling and one of the frequency higher with respect to the other one

I have read Rigorous justification for rotating wave approximation to have an idea of a rigorous proof of RWA approximation. The main idea I have from this is that you can see it if you write a ...
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Approximating ground-state energy without using variational principle

Given the Hamiltonian for one dimension harmonic oscillator: $$H=-\frac{\hbar^2}{2\mu}\frac{d^2}{dx^2}+\frac{\mu\omega}{2}x^2 ,$$ I need to calculate the approximate ground state energy using the ...
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1answer
63 views

Relation Between Cross Product and Infinitesimal Rotations, Generators, Etc [duplicate]

Looking into the infinitesimal view of rotations from Lie, I noticed that the vector cross product can be written in terms of the generators of the rotation group $SO(3)$. For example: $$\vec{\mathbf{...
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1answer
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Rotating wave approximation and classical Rabi oscillations: why don't the fast oscillating terms seem negligible in the initial frame?

I am trying to understand better the rotating wave approximation (RWA). Consider an atom modeled as a two level system, interacting with a Laser. I have the dipole momentum operator $$\vec{D} = d \...
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4answers
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Why is $\exp \left ( \frac{\pi}{2\hbar}(L_x^2 + L_y^2) \right )$ not a unitary operator? [closed]

I should prove that $$\exp \left ( \frac{\pi}{2\hbar^2}(L_x^2 + L_y^2) \right )$$ is not a unitary operator. Where $L$ is the total angular momentum of a 2-particle system ($L = L_A + L_B$ for the ...
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What is a definition of the trace norm?

I have found that (one?) definition of the trace norm is $$\mid\mid A\mid\mid = \sqrt{A^*A} \tag{1}$$ but now I am reading this paper where (on page 4) it says In particular, we will restrict ...
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The fine structure constant and the strength of interaction between two particles

In my notes, the following is mentioned: We consider the scattering of a beam particle with energy $E$, momentum $p$ and charge $ze$ off a charge distribution $\rho (x)$ of total charge $Ze$. We ...
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1answer
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From the perspective of QM, how can a thermodynamically isolated system can have a constant internal energy $U$?

In thermodynamics, we assume that an isolated system has an internal energy $U$, and if there is no heat given, or work done by/to the the system, this energy is constant. However, in QM, we do know ...
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In particle colliders, according to QM, how are two particles able to “collide”?

According to QM, we know that The act of measurement forces a particle to acquire a definite (up to experimental errors) position, so in a particle collider, like the one in CERN, by which means ...
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Getting $h_x, h_y, h_z$ Components of Hamiltonian after Gauge Transformation

In Fruchart et al.'s An Introduction to Topological Insulators, the Bloch Hamiltonian for a two-band insulator is given in the general form $ H(k)= $ \begin{bmatrix} h_0+h_z & h_x-i h_y \\ ...
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2answers
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Can an electron of an atom be found anywhere? Does it need energy to happen? [closed]

According to quantum mechanics it should be possible. But can it happens when it has so small probability to occur? also if it can happens that means that energy must be provided in order to the ...
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1answer
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Probability of WaveFunction [closed]

A particle is confined in a one dimensional box of length $a$. What is the probability of finding the particle at $x = a/4$? I know that the wave function is written as $$y= A\sin([(\pi x)/a]$$...
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Mistake in “Quantum Mechanics” by Auletta, Fortunato and Parisi?

On page 200 of Auletta, Fortunato and Parisi's textbook on Quantum Mechanics they write: \begin{equation} \hat{\mathbf{l}}^2|l, m_l\rangle=l(l+1)|l, m_l\rangle \tag{6.31} \end{equation} ...
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1answer
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Volume per $k$-state

We're talking about Fermi-energies for the first time, for $N$ spin $\frac{1}{2}$ particles in a 3D box, and she writes down that $$2 \times \frac{1}{8} \times \frac{4}{3} \pi k_f^3 = Nq \times \frac{\...
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1answer
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How do Fermions with $0$ weak hyper charge couple to electro-weak force?

If you have two fermions (with spin $\pm \frac{1}{2}$) that form a weak-isospin doublet and their respective right-handed fermions which are weak-isospin singlets, what would it imply if the doublet ...
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1answer
32 views

Why is it that when the atom has inversion symmetry, its dipole moment vanishes when the atom is in an eigenstate?

I am now reading my lecture notes on dipole moment and there's a point which confused me. It says that: Let us consider the $|1s\rangle$ and $|2p_x\rangle$ states of a hydrogen atom. The atom has ...
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1answer
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If both the eigenvector of $S_z$ and $\hat x$ form a basis for our Hilbert space, how can it have different dimensions?

In almost all the books on Quantum Mechanics, it is stated that if $|\alpha \rangle $ is a ket describing the state of a system, then any observable has a set of eigenvectors s.t those ...
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Can global unitaries create entanglement?

So I am reading this paper, which states multiple times that: Indeed, global (and thus entangling) unitary operations are capable of extracting more work than local operations from a set of ...
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Does quantum mechanics superpositions mean that particles exist simultaneously in all the states? [duplicate]

I will give a few examples to explain my question: Suppose we send a beam of light through a beam splitter which splits the beam into upper and lower branches . Then they interfere constructively and ...