Questions tagged [quantum-mechanics]
Refers to the branch of mechanics that deals with the mathematical description of the motion and interaction of subatomic particles, in particular electrons.
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What are the observables when a quantum system is comprised of orthogonal spacetimes?
We are given a system of three quantum domains A, B, and C with the following properties:
(1) domains A and B are independent Hilbert spaces, each with their own space and time dimensions. Both are ...
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Clarifying local magnetic moment axes in VASP: cartesian vs crystal (for MAGMOM/M_CONSTR)
In VASP, one can set the local magnetic moments of each ion in a non-collinear SOC calculation along a certain direction using the MAGMOM/M_CONSTR tags. The manual linked to states that these local ...
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To what extent can coarse-grained models retain the essential quantum mechanical characteristics of a system?
To what extent can current coarse-grained models, within the context of multiscale modelling, retain essential quantum mechanical characteristics such as electron correlation, polarization, and ...
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Which is better? Rashba effect or Dresselhaus effect?
My current research focus is on the band splitting observed in 2D perovskite. Existing literature suggests that site inversion asymmetry (SIA) may lead to the Rashba effect, while bulk inversion ...
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Symmetric issue about the Gaussian basis Hamiltonian
The material system is described by the Hamiltonian and overlap matrice, with the Gaussian basis set.
At Gamma point in the reciprocal space, the upper triangle block and the lower triangle block in ...
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Why is chemical bond dissociation difficult to simulate?
I'm a student doing quantum computing research trying to understand better what kinds of chemical systems are difficult to simulate on a classical computer and for which quantum simulation could be ...
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Script to draw one-dimensional PES comparing harmonic and anharmonic vibrational modes
This is an extension of a question I asked a little while ago: Software to draw one-dimensional PES including vibrational energy levels. I am asking the followup here based on advice received after ...
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Time Evolution of the Hartree-Fock Wave Function
The Hartree-Fock Hamiltonian is given by
$$
\hat{H} = \sum_i \hat{h}_i + \frac{1}{2}\sum_i\sum_j \left[\hat{J}_{ij} - \hat{K}_{ij}\right]
$$
and by choosing a basis, the Hamiltonian can be written in ...
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Why, if the potential is different from the Coulomb one, but has spherical symmetry, the eigenvalues of the system are non-degenerate? [closed]
Question duplicated from here https://mathematica.stackexchange.com/questions/287433/why-if-the-potential-is-different-from-the-coulomb-one-but-has-spherical-symme and here https://physics....
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Can we download DMol3 for free?
I want to try using DMol3 software for my research studies of doing optimisations and DFT calculations. Anyways I was unable to find a download link. Is it available for free? if so can anyone please ...
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How can one determine the time-step for imaginary time evolution?
The real-time evolution of a quantum system described by the state $\psi(t)$ is formally given by,
$$ \psi(t+\Delta t) = \exp^{- i \hat{H} \Delta t / \hbar} \psi(t)\tag{1}$$
For dynamical simulations ...
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How To Extrapolate Ground State Energy in Thermodynamic Limit via DMRG [closed]
I am implementing a system of fermions in a trap potential with tensor networks and want to find the ground state energy via DMRG (I'm using SyTen). As usual in quantum chemistry the Hamiltonian has ...
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Is it possible to model hBN spin defects/plasmons coupling in COMSOL/Lumerical
Hexagonal Boron Nitride (h-BN) is a promising material for Quantum technologies, see [1]. I want to perform a plasmonic simulation in COMSOL to replicate this paper. But I am not able to find any ...
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Density Functional Perturbation Theory
What is the difference between density functional perturbation theory (DFPT) and many-body perturbation theory (MBPT)? Also, please help me understand why approximations like PBEsol are considered as ...
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Kohn anomaly and avoided crossing (or anticrossing/level repulsion) [closed]
Kohn Anomaly and Avoided Crossing (Anticrossing/Level Repulsion) are terms that are found to be used when discussing phonon dispersion. The former (see last paragraph, page 198) is related to electron-...
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Understanding the complexity of geminal-based wavefunctions
Cross-posted on Reddit.
I have been reading through [1] to get a better understanding of geminal-based methods. Some short passages are included below:
The occupation of each orbital in the expansion ...
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How to apply solvent-correction to Gaussian derived Gibbs energies?
I study reaction A + B → C + D in a water using DFT. I think I should apply some kind of correction over RRHO because it is not true in a solvent. I found the given work (https://doi.org/10.1021/...
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How do I get the wavelength of light from a diffraction experiment using Python? [closed]
What is the procedure after using a diffraction grating (device used to see the spectrum) using python? We would see the entire electromagnetic spectrum emitted by an object but what then? how do I ...
user6553
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Equation (4) in Hohenberg-Kohn Paper
In their landmark paper of 1964, Inhomogeneous Electron Gas, Hohenberg and Kohn wrote down:
We shall be considering a collection of an arbitrary number of
electrons, enclosed in a large box and ...
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How do scalar states with different multiplities make spin-forbidden reactions possible?
This question is related to How spin-orbit coupling makes spin-forbidden reactions possible? - Matter Modeling Stack Exchange
Even more importantly, [H,S2]=0 fails for multi-electron systems even ...
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How spin-orbit coupling makes spin-forbidden reactions possible?
My question is related to the Wikipedia page of spin-forbidden reactions https://en.wikipedia.org/wiki/Spin-forbidden_reactions
When a reaction converts a metal from a singlet to triplet state (or ...
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What is a "transient" state?
I was analyzing this source code of the Ising model. I found the term "transient state".
I also found the term in this text:
There are two absorbing states in this Markov chain because once ...
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What is the best algorithm for ERIs of contracted gaussian atomic orbitals
I am currently working on python script that does Hartree-Fock-Calculations. I try to avoid packages as good as possible. I've figured out how to calculate the one electron integrals when it comes to ...
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What occupation should be used for non metallic energetic materials in Quantum espresso?
I am trying to understand the Quantum espresso input file and I intend to do DFT calculation on an Energetic material (TKX-50) consisting of C, H, O, AND N. I have seen that "smearing" ...
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Cross-post: Matrix elements <n,k|x|n',k'> for Bloch states
Cross posted at Physics.SE
I believe this is just elementary QM, but I'm getting awfully confused. The question is drawn from this paper on Wannier-Stark localization (but is self-contained).
Let:
\...
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Green function KMS boundary condition [closed]
How to obtain the relation between $G_{ab}(\tau,0,0,0)$ and $G_{ab}(\beta-\tau,0,0,0)$ for two-particle fermion Green function
$$G_{ab}(\tau_1,\tau_2,\tau_3,\tau_4)=\langle \mathcal{T}a^\dagger(\tau_1)...
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How are the exponents in a STO-nG basis set obtained?
STO-3G has exponent parameters which can be found in a reference book. Can these parameters be calculated using, for instance, a Hartree–Fock equation for one atom? Or using another way?
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What does it mean when the first order correction energy is 0?
Suppose I have the following Hamiltonian to start
$$ H_0 = \begin{pmatrix} 0 & 0 & 0 & 0\\ 0 & 0 & 2 & 0\\ 0 & 2 & 0 & 0\\ 0 & 0 & 0 & 0 \end{pmatrix} $$...
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Do we know for sure that all atomic and molecular wavefunctions decay exponentially as r goes to infinity?
Slater type orbitals (STO) are considered to be more accurate than gaussian type orbitals (GTO) for atomic and molecular QM calculations because - among other reasons - they decay with $e^{-\alpha r}$ ...
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How to numerically calculate quantum state distance using quantum metric?
In Ran Cheng's review of the quantum geometric tensor, eq. (11) gives the tensor as:
$$
Q_{\mu\nu}=\sum_{n\neq 0}\frac{\langle\phi_0|\partial_\mu H|\phi_n\rangle\langle\phi_n|\partial_\nu H|\phi_0\...
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How to solve time-dependent Schrodinger equation and plot trajectory on Bloch sphere?
Let's say I have a $2 \times 2$ Hamiltonian that I am solving using the time-dependent Schrodinger equation:
$$
i \frac{d}{dt} |{\Phi}\rangle=H|{\Phi}\rangle.\tag{1}
$$
Consider a generic Hamiltonian
$...
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Calculating the excited state dipole moment
I am trying to calculate the dipole moment of an excited state, using "Gaussian" software. My input commands were:
...
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Electric quadrupole operator for periodic systems
Considering one component of the electric quadrupole operator $\hat{r}_x \hat{r}_y$, I'm wondering if the following equalities hold:
$$
\langle u_{n\mathbf{k}} | \hat{r}_x \hat{r}_y |u_{m\mathbf{k}} \...
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Quantum mechanical antireflection coating; what quantity would be analogous to index of refraction?
Background
Quasiparticle interference (QPI) is a technique that can be used to study 2D surface state band structure; carrier reflections at boundaries or impurity sites will interfere producing ...
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How to get energy eigenstates using plane wave basis wavefunction .hdf5 output from Quantum ESPRESSO? [closed]
When compiled with the HDF5 flag on, Quantum ESPRESSO (QE) saves wavefunctions in the .save folder. At each k-point, we have an $m\times n$ matrix, where $m$ are the complex number entries of ...
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Ground State energy trick for many-body electronic structure calculations?
I am an outsider to this field, so I am not sure about the validity of my work below.
Let us define the following Hamiltonian from DFT:
$$ \tag{1}H_{ij} \psi_{ij} \equiv (-\frac{\hbar^2 \nabla_i^2}{2m}...
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How to formulate the second quantization of Dzyaloshinskii-Moriya interaction?
The Dzyaloshinskii-Moriya interaction (DMI) existing in the interface of the ferromagnetic insulator and the metal with strong spin-orbit coupling (SOC) is shown below.
Mathematically, it can be ...
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Tools for symbolic calculations of quantum transport using the Keldysh NEGF formalism [closed]
I am looking for tools for symbolic calculation of quantum transport or quantum mechanics that involves Keldysh NEGF (non-equilibrium Green's function) formalism. The closest tool I heard/seen is <...
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Confusions in interpreting Dirac strings (wormholes) in Haldane's Hilbert space picture ft. two tori joined by strings at gapless points
I had a question about Haldane's wormhole interpretation (picture below). I believe he first proposed it in his paper Berry Curvature on the Fermi Surface: Anomalous Hall Effect as a Topological Fermi-...
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Help with definitions in k-space twisted bilayer graphene model
I am trying to numerically do calculations using Eq. 8 of MacDonald's simple model for twisted Bilayer graphene. I only want to calculate the Berry phase. However, I don't think I have my definitions ...
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Valleys and time reversal symmetry (Zeeman effect)
Right now I'm focused on transition metal dichalcogenides. These compounds in the Brillouin zone have valleys in the valence band and in the conduction band at points K and -K. From what I've seen of ...
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Example of 2D k-space models allowing interband transitions after a closed-loop trajectory? [closed]
I have been mainly exposed to 2D momentum-space condensed matter models in the context of Berry-related topology. I now want to study models where, if I take a closed loop in momentum space, I will ...
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Help with translating Hamiltonian into matrix
Eq. 19 in this paper gives the following Hamiltonian:
$\sigma_a, \tau_a, \eta_a$ are respectively the spin, sublattice pseudospin and valley pseudospin respectively.
Normally, I would have chosen a ...
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Help with Definitions in Numerical Calculation of Multiband Berry Phase
In the third chapter of Vanderbilt's book, they discuss the so-called multiband parallel transport and provide a scheme for numerical calculations that is similar to the single band case (where the ...
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How to numerically solve real-space 1D time-independent Schrodinger equation using 2D momentum-space Hamiltonian?
Consider the usual simple 2-level graphene Hamiltonian with mass in momentum-space where:
$$
H(k,V)=-t \sum_{\delta} [\cos(k\cdot\delta)\sigma_x-\sin(k\cdot\delta)\sigma_y+V\sigma_z],
$$
where $t$ is ...
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Help with understanding topologically-protected edge states in domain wall systems
Let's say that I have a simple domain wall system for the following Hamiltonian with added on-site potential $M(x)$:
$$\tag{1}
H(k,M)=-t \sum_{\delta} [\cos(k\cdot\delta)\sigma_x-\sin(k\cdot\delta)\...
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How to determine which levels correspond to each other in LS coupling and jj-coupling?
In the LS coupling scheme, L, S and J are good quantum numbers; whereas in jj-coupling scheme, j1, j2 and J are good quantum numbers. I have learnt how to get the term symbols for LS coupling, and for ...
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How are molecular rotational states modeled within the Born Oppenheimer Approximation for polyatomic molecules?
Molecular vibrational states associated with an adiabatic electronic state within the Born-Oppenheimer Approximation are typically defined by doing the harmonic approximation for the potential at an ...
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What does “strongly correlated” mean?
For quantum many body problem, there is a common terminology “strong correlated systems” that appears in different context. However, it seems that the definition of it is ambiguous and sometimes ...
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How can we say that the KS equation is describing a noninteracting many-electron system?
Based on HK's two theorems, the density functional theory was built. Because one can't find the universal energy functional $F_{HK}[n(r)]$, Kohn and Sham further proposed the Kohn-Sham ansatz: mapping ...
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