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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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Variation of the Palatini action with respect to the triad and spin conection

I am trying to understand how could we get these two equations of motion by varying the action with respect to the triad and spin connection. The lecturer gave a hint that we can use integration by ...
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Probability of finding a particle in a two/three particle system

Let us consider a system of 2 identical paricles, 1 and 2. Let, ψa(1) is the amplidude of finding particle 1 at state a, and ψa(2) is the amplitude of finding particle 2 at state a. Let N.F is an ...
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Why are more massive white dwarfs smaller?

I understand that a neutron star is supported by the pauli exclusion principle and that the larger the gravitational force against them, the closer the electrons must pack. But I have 2 queries, one ...
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60 views

What had Feynman meant when he told nobody understands Quantum mechanics? What do we mean by understanding Quantum mechanics?

What had Feynman meant when he told nobody understands Quantum mechanics? What do we mean by understanding Quantum mechanics?
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20 views

Galilei group and Constrained QM

Let's assume spin-0 for simplicity. So far as I understand the issue, the Galilei simmetries constraints the possible hamiltonians of a quantum systems so that the only possible interactions of a ...
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Stern–Gerlach - Sequential experiments

Could someone please explain this experiment to me? Why depending on the orientation of the apparatuses, we get different results? For example why if we have $z,x,z$ (I am not sure what is the correct ...
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Weinberg quantum mechanics [on hold]

Can someone provide me the solution manual of lectures on quantum mechanics by weinberg. Some of the problem is really too hard to solve
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WKB Approximation on Shelves in the Middle of an ISW

I have just finished my second semester of Quantum Mechanics! Woot! On our final test we had a very straightforward WKB problem which was straight out of Griffith's. (8.1 in 2e and 9.1 in 3e) It was ...
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25 views

Mean kinetic energy without full laplacian

I need to calculate by solving the integrals the expectation value of the kinetic energy $\hat{T}$ and potential energy $\hat{V}$ operators in the state $\Psi$, defined as $$ \Psi(r) = \sqrt{\frac{1}{\...
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Derivation of the de Broglie waves for a relativistic particle

Generally speaking I am looking for the derivation of the de Broglie waves for a relativistic particle. The particle is in electric field potential ($U$) which accelerates the particle as well. Let's ...
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Is people's life deterministic or random? [on hold]

Is people's life determined because of the standard physics or random because of (for example) quantum mechanics? I’m not asking if i can know what will happen, but if it's already determined somehow?...
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Is the universe a closed system?

Most places say it is. But according to the multiverse hypothesis, gravitons and other quantum particles could travel from one universe to another. Wouldn't matter-energy then be transferred and thus ...
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Entanglement breaking quantum channels

An entanglement breaking quantum channel is defined as one where $\sigma_{AB}=(\Phi_A\otimes I_B)(\rho_{AB})$ is separable, even for entangled inputs $\rho_{AB}$. Of course, if the input $\rho_{AB}$ ...
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Somehow unexisting book even though volume 2 exists

I am desperately trying to find a book Electromagnetic Interactions of Hadrons, Vol.1, A Donnachie; G Shaw; New York 1978 Somehow, the second volume is easily ...
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19 views

Canonical and grand canonical formalism at zero temperature

How do we find expectation value of any operator at zero temperature in quantum statistical mechanics formalism? Expectation value of any operator $\hat{O}$ is given as $$\langle \hat{O}\rangle = Z^{-...
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Finding number of photons per second crossing an area with distance ${}d$ from a radiating point

Estimate the number of photon per second entering one eye of the observer from 10 Watt red light source at 50m away form point source.
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How to efficiently compute the commutator $[\hat{r},\nabla^2]$?

Given a system with Hamiltonian $ \hat{H} = \frac {\hat{p} ^2}{2m} + \hat{V}(r)$ in a certain state $|\psi \rangle$, I want to find if $\langle r \rangle$ varies with time. From $$ i \hbar\frac {d ...
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61 views

In QM does the observer really perturb the system to make a measurement?

It is commonly taught in introductory QM courses that in order to get to know the position or momentum of a particle, be it by "sending a photon" or similar experiments, the measurement necessarily ...
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Pauli Exclusion Principle and Identical Fermions

Pauli exclusion principle means no two identical fermions can be in the same quantum state. Does it mean, two electrons with the same spin cannot be in the same De Broglie Wavelength? Or, more ...
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Other than polarization what hidden variables have been applied to pairs of particles to correlate them? [on hold]

What correlated systems have been offered to produce quantum mechanical predictions? Are there any examples?
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Why can an inner product of an eigenvector also be used as an eigenvector?

In quote box below, there is an inner product of an angular momentum eigenvector. Why can you use this inner product as a new eigenvector for the next part of the work? And why do they "of course" ...
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1answer
378 views

Is the Born rule indeed wrong?

This is a question about the validity of a preprint, arXiv:quant-ph/0509089, which claims that the "Copenhagen Interpretation of QM is incorrect" (same title, authored by Guang-Liang Li and Victor O.K....
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1answer
35 views

Substituting into quantum harmonic oscillator

I'm a bit confused by the substitution that is often performed with the harmonic oscillator. This step is usually skipped over, but it has me a bit confused. I attached a picture to show what is ...
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1answer
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Is there a systematic method to derive Bell's inequalities?

BACKGROUND The purpose of Bell's inequalities is to put bounds on certain combinations of classical measurement probabilities. One can then show that quantum entanglement can yield probabilities that ...
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Ohmic spectral density

I am witting a paper about the non-Markovian effects of open quantum systems (a qubit interacting with a bosonic environment). I am using a spectral density of the form below: $$ J(\omega) = \frac{\...
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Introduction to symmetries in physics

What are the topics that i should read after doing a course on classical mechanics,covering most of Goldstein {except continuum mechanics}to learn {more,as a beginner} symmetries related to classical ...
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Connection between Classical and Quantum symmetries

I am an advanced undergraduate student.I would like to know about the importance of symmetry in classical and quantum mechanics.Also a good book concerning the connection between symmetries of ...
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19 views

Feynman diagram combinator and multiplier value

Dear experts, I try to learn by self feynman diagram from examples of x^3 and x^4 for first and second order consolidated from different reading material. For x^3, combinator values of 3 * 3 for n=1 ...
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Energy Functional vanishing to first order

I am trying to show the energy functional vanishes to first order: $$\int d^3r[\frac{\hbar^2}{2m}\nabla(\Psi+\delta\Psi)\cdot\nabla(\Psi+\delta\Psi)+V(\vec r)(\Psi+\delta\Psi)^2].$$ For the $\int\...
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21 views

What is the practical Length of photons, in vacuum for example [duplicate]

From practical point of view we know the width of photons is proportional to wavelengths (experiments for light going through tiny holes: it starts with a specific size of the holes, etc). And nobody ...
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1answer
58 views

Interpretation of the wave function in newtonian spacetime

A Newtonian spacetime is a quintuple $(M, \mathcal{O}, \mathcal{A}, \nabla, t)$ where $(M, \mathcal{O}, \mathcal{A}, \nabla)$ is a 4 dimensional differentiable manifold with a torsion free connection, ...
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1answer
56 views

Defining a metric on the space of paths

Imagine the following path integral $$\int_{x(0)=x_i}^{x(T)=x_f} \mathcal{D}x \, e^{\frac{i}{\hbar}S[x]}.$$ This integral is defined over the space of all paths that satisfy the boundary conditions ...
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What is the source of the difficulty (within the variational approach framework) in the attempt to unify quantum mechanics with general relativity? [duplicate]

It seems to me that quantum mechanics can be formulated within the general mathematical framework of variational  principles. Derivation of the equations of nonrelativistic quantum mechanics based on ...
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Can we create a random variable using QED effects?

Quantum Electrodynamics (QED) has some observable effects such as the lamb shift, which is mainly caused by the vacuum polarization and the electron self-energy. These effects contribute to the "...
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2answers
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Precise definition of the Hilbert space in QM?

In QM books (at least those I have read) the definition of the Hilbert space used is somewhat blurred (the "space of square integrable functions" is not enough to define it precisely : which kind of ...
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Could a solid object made entirely of antimatter safely “touch” ordinary matter without annihilating each other because of EM force?

Most is said about the anti-particles annihilating their ordinary particles counterparts. When antimatter forms anti-atoms, it is said they behave like ordinary matter. Since atoms are more stable ...
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Wavefunction collapse in Stern-Gerlach experiment

Consider silver atoms coming from an S(X) apparatus, after S(X) apparatus we place an S(Z) apparatus $$ |\mathrm{SX+}\rangle= \frac{1}{2}|\mathrm{SZ+}\rangle + \frac{1}{2}|\mathrm{SZ-}\rangle, $$ ...
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Most influential theories in fundamental physics during the last decades? [on hold]

As a mathematician, I am interested in understanding as much as posible of the last works in theoretical physics (particularly the different ways of unifying GR and QM). Could you tell me the main ...
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Wave function collapse and a general wave function

Action of an operator on a state vector collapses the wave function to any of the eigenstate of that operator , So we get resulting state of the system as some base ket. But mathematically action of ...
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Correlated quantum systems

I am working on correlation in quantum systems and would like your comments regarding correlation in quantum systems and to fill the gap in the proofs or to use another type of such relations with the ...
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1answer
61 views

Proof for $\langle i[A,B]\rangle$

I have to prove the following equation: $$ \langle i[A,B]\rangle = 2\mathfrak{Im}\left[\int dV(\overline{B\psi)}(A\psi)\right]\,,$$ where A,B are hermitian operators. Here is my calculation, but I don'...
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How to understand notation in “Introduction to Quantum Mechanics (3rd Edition)” by David Griffiths, Chapter 3.6.2?

In the 3rd edition, on page 118, the projection operator is introduced as $$\hat{P}=|\alpha\rangle\langle\alpha|.$$ Then Griffiths says that when $\hat{P}$ acts on another vector, it looks like ...
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Young's Double Slit, phase difference and path difference

To produce an interference pattern, the light sources must be coherent right? Coherent by definition means constant phase difference between waves of the same frequency so that means waves can be ...
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1answer
52 views

Quantum statistical mechanics formalism

How do we solve a Hamiltonian written in second quantization by using quantum statistical formalism? For example, the following Hamiltonian $$H = \sum_{i=1}^L c_{i+1}^\dagger c_i + h.c.$$ I have ...
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Derivation of Hamiltonian of EP-modulated microring resonator

I'm an undergraduate in a nanophotonics lab and I need to derive something for my PI, but don't exactly know how to go about it. When reading a relevant paper, it was given that the Hamiltonian of an ...
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42 views

Example of calculating phase shifts in scattering theory

I have an extended question to this post: Phase shifts in scattering theory I have read it and also went over the formalism in Sakurai's, Shankar's, and Griffith's. I am now trying to look for ...
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Transient solution system of differential equations obtained from master equation

I have to solve the following equation (or at least obtain an approximate estimate) for the diagonal terms of the density matrix. We consider that the initial state is a coherent state $\rho_{n,n}(0)=...
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Source for mathematical methods [duplicate]

I am just curious about any question and example sources for linear vector spaces, bra-ket notation, operators, commutators and hilbert spaces.
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1answer
47 views

Well-definedness of Holstein-Primakoff transformation

In many-body physics, Holstein-Primakoff transformation is defined as follows: \begin{align} S_i^+ &= \sqrt{2S}(1-a_i^\dagger a_i/2S)^{1/2}a_i, \\ S_i^- &=\sqrt{2S}(1-a_i^\dagger a_i/2S)^{1/2}...