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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11
votes
1answer
238 views

How exact is DFT, really?

It is often claimed (e.g. here), that Density Functional Theory is in principle exact. This seems to be a very strong statement to me. Are all current limitations only of a technical nature rather ...
16
votes
1answer
968 views

Does the Schrödinger equation have unique solutions?

I am learning DFT and the Hohenberg Kohn Theorem of Existence. It says that there is a one-to-one correspondence between the external potential and the density. However the proofs that I have seen ...
6
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0answers
42 views

Evaluating $C_v$ for one mole $H_2$ molecules in a quantum simulation [closed]

Given an ensemble of $N$ diatomic molecules, we know that the rotational partition function is given by $$Z_r = z_r^N$$ where $$z_r = \sum_{l} (2l+1)e^{-Kl(l+1)}$$ where $K = \beta \hbar ^2 /2I$. I ...
12
votes
1answer
162 views

How to explain Density Functional Theory results to an experimentalist?

When we present our Density Functional Theory simulation results e.g. lattice parameters, stacking fault energies, band gaps, etc. to people who are experimentalists then the very first question ...
6
votes
1answer
103 views

Velocity operator for a Hamiltonian that satisfies the generalized Schrodinger equation

The velocity operator is defined as $\mathbf{v}=i[H,\mathbf{r}]$ for the Hamiltonian $H$ satisfying $H\psi=\epsilon \psi$. This can be obtained from the Ehrenfest theorem. I'm wondering if $\mathbf{v}=...
10
votes
1answer
386 views

Which method gives the most accurate electron density, and how can it be verified experimentally?

I read a paper from Science (DOI https://doi.org/10.1126/science.aah5975), “Density functional theory is straying from the path toward the exact functional”. They were trying to make a point that ...
3
votes
1answer
35 views

Interpretation of electronic band structure diagram

I want to understand the electronic band structure diagram of the following image, corresponding to $\text{MoS}_2$ (TMD): I read about DFT (density functional theory). DFT is based on solving the ...
9
votes
0answers
84 views

Hamiltonian of TMDs - derivation

TMDs are transition metal dichalcogenides and have the chemical formula MX$_2$ where M is the transition metal and X is the chalcogen. An example of a TMD is MoSe$_2$. I would like to demonstrate that ...
10
votes
1answer
92 views

Anomalous Quantum Hall Effect

I am studying the transition metal dichalcogenides (TMDs) and I have seen webinars and articles that said that these materials exhibited the anomalous quantum Hall effect related to the curvature of ...
7
votes
0answers
43 views

Adiabatic equation related to the Berry phase for $\lambda$ with first order terms

The wave function for the adiabatic approach is as follows: \begin{equation} |\psi(t)\rangle=e^{i\phi(\lambda(t))}e^{-i\gamma(t)}|n(t)\rangle \tag{1} \end{equation} where $e^{i\phi(\lambda(t))}$ is ...
9
votes
2answers
267 views

Dynamic phase in an adiabatic system

I am trying to understand the Berry phase through the evolution of a system that evolves adiabatically. Schrodinger's equation is: \begin{equation} H(\lambda)|n(\lambda)\rangle=E_n|n(\lambda)\rangle \...
9
votes
2answers
378 views

Can Machine Learning lead to the more accurate theories and methods for matter modeling?

There's no doubt about it. Machine Learning (ML) is one of the hottest topics out there and it plays an important role in computational science. One application I have seen is to use ML and Density ...
7
votes
1answer
84 views

What are the types of Quantum Molecular Dynamics (QMD)?

In similar spirit to recent questions on Quantum Monte Carlo, ab-initio Molecular Dynamics, types of SCF, and others, I would like to ask: What are the types of Quantum Molecular Dynamics (QMD)? As I ...
5
votes
1answer
33 views

Property related with Berry curvature: $\Omega_{n,\mu\nu}=-\Omega_{n,\nu\mu}$

I read in David Vanderbilt's book named "Berry Phases in Electronic Structure Theory - Electric Polarization, Orbital Magnetization and Topological Insulators" the definition of Berry ...
17
votes
1answer
113 views

Derivation of Slater-Koster equations

I am trying to derive the Slater-Koster equations (Table. 1 of Ref. 1) for the two-centre approximation of hopping integrals between atomic orbitals. I understand that Slater-Koster approximates the ...
14
votes
1answer
68 views

On mass polarization terms

In Jensen's Introduction to Computational Chemistry it says that the total non-relativistic Hamiltonian operator, transformed to the center of mass system, can be written, in atomic units, as $$ \hat{...
19
votes
1answer
93 views

How is Poier and Jensen's Bond Capacity Model Parameterized and Optimized?

I am working on adding a charge polarization model into my own research and have been exploring a few approaches. One of the most attractive options is the Bond Capacity (BC herein) model of Paolo and ...
17
votes
3answers
196 views

How are continued fractions related to quantum materials?

In my spare time, I have been studying and analysing continued fractions. I was having a conversation with someone on Discord in a Mathematics server and he was telling me that continued fractions ...
26
votes
5answers
250 views

What are the situations/problems where Born-Oppenheimer approximation is invalid?

We use the Born-Oppenheimer approximation in both Hartree-Fock method and DFT. What are the problems where we cannot use this approximations.