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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Violation of time reversal symmetry

Can anyone please provide me with an example of unperturbed Hamiltonian for a certain physical system, which has no time-reversal symmetry, the only condition is that the spectrum of unperturbed ...
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Scattering problem with spin

My question is how to enter spin in the scattering problem? The simplest example is: consider two spin-$\frac12$ particles and the following potential: $ V(r) = \sigma_1.\sigma_2 \frac{e^{-\lambda r}}...
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How to calculate the amplitude of a matter wave of debroglie equation?

I studied the formula that to calculate the wavelength of a matter wave we have to calculate $h/p$ where $h$ is plancks constant and $p$ is the momentum of the particle for which we want to calculate ...
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Pertubation Theory

For long-range barrier tunneling, consider three qubits governed by the Hamiltonian $H$. $$ H = -J(\sigma_1^+\sigma_2^-+\sigma_1^-\sigma_2^++\sigma_3^+\sigma_2^-+\sigma_3^-\sigma_2^+)+\frac{U}2\sigma^...
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How to show that a system of even number of Fermion has integer spin?

I am informed that a system of even number of fermions has integer spin. I don't know how to show it with creation and annihilation operators.
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Does thermodynamics predict the effect of spontaneous emission (QED)?

Could one say that spontaneous emission is expected from thermodynamics, as a isolated atom needs a relaxation process to the ground state to reach equilibrium at low temperatures?
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Quantum key distribution

Key advantage in quantum key distribution is using quantum channel. (The quantum channel is preserve coherent superposition of quantum bit of information). what is means (The quantum channel is ...
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Experiments with particle and light that I don't understand [closed]

I have these following two experiments that seemed not so clear for me Michelson Morley experiment - The first one is the experiment from Michelson and Morley who proved (if I'm not wrong) that the ...
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Frequency shift of Duffing oscillator with Boltzmann-distributed amplitude

Say I have a duffing oscillator without a driving force or a damping: $$ \ddot x + \alpha x + \beta x^3 = 0 $$ This leads to the frequency response $$ \left[\omega^2 - \alpha - \frac{3}{4} \beta x_0^2\...
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Textbook recommendations for teaching a 300-level (sophomore/junior undergrad) Modern Physics class from? [closed]

I'm a Prof who is trying to find a better text-book for my (300-level) Modern Physics Class. Currently I'm using Tipler & Llewellyn, but it's pretty terrible and plus it's out of print. Anyone ...
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Lenses and uncertainty principle

I saw a video explaining the central fringe width of a single slit diffraction pattern with the uncertainty principle. It explained: as the slit size decreases, the uncertainty of the position of ...
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Measuring momentum

I'm new here, possibly my apologies for misplacing. After a measurement in quantum mechanics, the wavefunction collapses to an eigenstate corresponding to the outcome of the measurement. Thus if we ...
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Energy in interaction hamiltonian and energy levels in pump probe experiments

Consider a two-level system described by the hamiltonian $H = \hbar \omega_{eg} /2 \sigma_z \quad (1)$ The eigenenergies are $\pm \hbar \omega_{eg}/2$. Now, we add an interaction with an ...
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Semiclassical approximation self-study

Can someone give a review of good books to learn semiclassical physics? Somehow, I would like to know if there is a text at the level of Lanczos or Gelfand. By this, I mean that I am interested in the ...
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Simple formula for conductivity in an insulator

I have seen cited without explanation the fact that an insulator with band gap $\Delta$ has conductivity $$\sigma = C e^{-\Delta / kT}$$ at temperature $T$. Could some one provide a derivation of this ...
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What is the reasoning behind this solution?

https://quantummechanics.ucsd.edu/ph130a/130_notes/node145.html A particle is confined to a box of length $L$ in one dimension. It is initially in the ground state. Suddenly, one wall of the box is ...
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Does conservation of energy across “worlds” explain probabilistic filtering of photons?

We can set up a light filter and a light source such that angling the filter may block out some/all of the light. For example, with a certain filter angle we might see that $30\%$ of the original ...
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Stability of electron spin outside of a magnetic field

This question is best phrased in terms of two experiments: If I were to take a stream of hydrogen atoms, and pass it through a magnetic field, then the stream would split into two, based on the spin ...
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Why is the speed of a quantum particle defined as coefficient of $t$ over coefficient of $x$?

I’m currently studying quantum mechanics from Introduction to Quantum Mechanics by Griffiths. In his free particle section, he says that the speed of a particle is the coefficient of $t$ over the ...
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Operator norm and Action

We define the norm of the operator as $\left\lVert A \right\rVert = \sup \frac{\left\lVert A\psi \right\rVert}{ \left\lVert A \right\rVert} = \sup \left\lVert A\psi \right\rVert$ for $A ∈ L(H)$. It is ...
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Converting Hamiltonian of a 2-atom basis tight binding model to k-space and finding its hopping factors (using Fourier transform)

Hi could someone please help in finding the hopping factors of this Hamiltonian and also explain how to do it. H = sin(Kx)/σx + sin(Ky)/σy + (m-2 (2- cos(Kx)- cos(Ky )) /σz 0<m<4 4<m<8
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How to derive the electric dipole spin resonance (EDSR) Hamiltonian in a slanting Zeeman field?

Background I have been reading through the Supplementary Notes from [1] and I am having some trouble understanding part of the derivation. To begin with, the paper describes a spin qubit within a 2D ...
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A Venn diagram for: (non-)locality, (non-)realism, (non-)contextuality, (non-)signalling, (dis-)entanglement

I recently asked a (yet-unanswered) question about the relationship between state-dependence and violations of realism. The more I read on the subject, the more I find myself digging deeper in a ...
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Can we handle the wave function as if it was a real valued function?

I am trying to analyze in general simple one dimensional QM problems. To be more specific let's consider this kind of Hamiltonian: $$H=\frac{\hat{p}^2}{2m}+V(\hat{x})$$ From this one we can derive the ...
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Feynman’s electron double slit experiment?

I have seen several questions on the site about this, but most of them get bogged down into new complex interpretations of quantum mechanics. For reference, I am a high school student just starting to ...
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Fermionic vacuum under a Bogoliubov transformation

Context: Consider a Bogoliubov-de Gennes Hamiltonian, \begin{align} \hat{H}_{BdG} = \sum_{j,k} \hat{\Psi}_j^{\dagger}H_{jk}\hat{\Psi}_k, \end{align} where $\hat{\Psi}$ is a $2n$-dimensional vector of ...
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Trying to prove that a propagator only depends on the difference of coordinates if our system has translational symmetry

As the title says, I'm trying to prove that if a system is translation invariant, then its propagator depends only on the difference of coordinates. That is to say $$K(\boldsymbol{x},\boldsymbol{x}';t ...
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Sum of coeficients

How to show that $\sum |c_{n}|^{2} = 1$ ? Where, $\psi = \sum <c_{n}|e_{n}>$ (completeness) and $e_{n}$ are the eigenvectors of the general operator $Q$ (with discrete spectra) I started as ...
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What's the transform of the state when using Fourier transformation of operators to diagonalize a Hamiltonian?

The off-diagonal term of the 1-D Bose-Hubbard model is : $K=\sum_l a_l^\dagger a_{l+1}+a_{l+1}^\dagger a_l$. We can diagonalize it by introducing the Fourier transformation:$a_l=\frac {1}{\sqrt{N}}\...
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Why does Quantum Mechanics use Linear Algebra? [closed]

I am currently doing Linear Algebra in hopes of one day tackling QM, and I need some motivation now to continue in this pursuit. The University I attend set this as a pre-requisite for QM. Now I have ...
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Quantum tunnelling time experiment, what would the times be either side of the barrier?

Having read Quantum Tunnels Show How Particles Can Break the Speed of Light in Quanta; I felt the need to ask some smarter people than I a question. Consider two pairs of rubidium emitters and ...
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Normalization of functions in function space

It is a well know question, be the function space $L_{2}(-\infty,\infty)$, evidently the eigenfunctions of $$i\frac{d}{dx}, X$$ are $$f = Ae^{-i \lambda x}, g=B \delta (x-\lambda)$$ respectively. ...
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How to use only parity arguments to derive selection rules for $X$ and $P$ operators?

Derive rules of selection between matrix elements of eigkets $|{l,m}\rangle$ and $|{l',m'}\rangle$ for the operator $\hat{X}$ and $\hat{P}$. Use only parity arguments. I now that that the elements of ...
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Slow converging in Monte Carlo due to Shell effect

While I was reading materials, the author mentioned that Monte Carlo converges slowly due to shell effect while filling the single particle states, but using a twisted boundary will make it go much ...
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What does it mean for a phase to be unstable due to quantum fluctuations?

Generally in the literature on quantum critical phenomena (as opposed to ordinary critical phenomena in statistical mechanics), there is the idea that quantum fluctuations can prevent ordering of a ...
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In fiber bundle picture of Berry connection, what is the vertical basis if the horizontal basis is the underlying parameter space?

In Ref. [1], the authors show how The geometric (Berry) phase is shown to have its origin in the nontrivial geometry of the fiber bundle: Hilbert space --—> space of states. The nontrivial ...
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1answer
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Deriving an Angular Momentum Commutator Relation using $ϵ_{ijk}$ Identities

I can show that $$ [\hat L_i,\hat L_j] = i\hbar\epsilon_{ijk} \hat L_k $$ where $\hat L$ is the angular momentum operator. But I'm struggling to show that $$[\vec a \cdot \hat L , \vec b \cdot \hat ...
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3d solutions for 1d Schrödinger equation?

The general Schrödinger equation in 3d is $$i\hbar\frac{\partial\psi}{\partial t}(\mathbf r, t)=-\frac{\hbar^2}{2m}\nabla^2\psi(\mathbf r, t)+V(\mathbf r)\psi(\mathbf r, t).$$ Now consider that $$V(x, ...
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How to prove that a state is pure if and only if it cannot be expressed as a convex combination

Define a pure state to be one that can be expressed in the form $ \rho = | \psi \rangle \langle \psi |$. How can we show that this is equivalent to $ \rho \neq p \sigma_0 + (1-p) \sigma_1 $ for any ...
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Change in the value of speed of light and the frequency of visible light

So, we know that Quantum Mechanics is needed because observation tends to disturb the system. Whenever we observe a quantum particle through our eyes, the EM radiation needed to observe it disturbs it....
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Quantum model of the atom

please note that I am a high school student trying to understand the quantum model of the atom; I have only the most basic understanding of quantum mechanics. I am trying to comprehend the wave nature ...
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Quantum particle spead to macroscopic size

Is there experimental evidence of a single, free massive particle wavefunction can spread in space to macroscopic size? Thanks for the answers
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Is This Hypothesis Correct?

I have constructed a thought experiment regarding whether the future is deterministic or not. It goes like this: Let’s take an Observer 100 light years away from earth. Now presently, if he looks at ...
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Given a collapsed state, can we derive the prior shape of the wavefunction?

More or less the title. Assume that we have found a box containing a completely isolated system of particles. We do not know for how long this system has been allowed to evolve. We do know what ...
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How to put laser field into the Hamiltonian of the Schrodinger equation of a 3-level quantum system?

I read a paper about using femtosecond laser to control a 3-level quantum system. The author wrote the Schrodinger equation for the system and wrote the expression of the laser field. But I still don'...
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Understanding Born's rule for non-hermitian Hamiltonians

Say I have a non-Hermitian hamiltonian, such as one might have in an incomplete description of a system where the states are allowed to decay. Then probabilities are not conserved since magnitudes ...
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Separation into $|\Psi_{CM}\rangle$ and $|\Psi_{R}\rangle$ in abstract representation?

Consider a two-particle system with Hamiltonian $$\hat H = \frac{(\hat{\mathbf p}^{(1)})^2}{2m_1} + \frac{(\hat{\mathbf p}^{(2)})^2}{2m_2} + V(\hat{\mathbf r}),$$ where $\hat{\mathbf r} = \hat{\mathbf ...
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Dual of IC POVM cannot be positive

I've read a claim about POVMs in my lecture notes, which I fail to prove. Hence, I would be grateful if some of you have some hints for me /can help me. Let $\{N_i\}_{i=1}^{d^2}$ be an informationally ...
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1answer
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Direct Series Solution Attempt of the Quantum Harmonic Oscillator

The non relativistic Schrodinger equation of the harmonic oscillator in dimensionless variables is $$\frac{d^2 \Psi}{d \xi^2} = (\xi^2 - k)\Psi$$ where $$k \equiv \frac{2E}{\hbar \omega}$$ According ...
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Physically, why is the ground state wavefunction of Neon be spherically symmetric?

For a may electron atom, a closed subshell structure implies $$L=S=0$$ and therefore also, $J=0.$ Therefore, the ground state wavefunction of such an atom is spherically symmetric because the rotation ...

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