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.
11
questions
12
votes
1
answer
306
views
What is the best program to manipulate numerical DFT wavefunctions to calculate custom matrix elements?
For pedagogical reasons, I am looking for ways to calculate quantum-mechanical quantities such as $\langle m | \dot{m}\rangle, \langle m | \dot{n}\rangle, \langle m | \ddot{n}\rangle$ using ...
- 2,131
10
votes
1
answer
210
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 ...
- 4,487
19
votes
3
answers
361
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 ...
- 243
17
votes
1
answer
1k
views
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 $e^{-\alpha r}$ ...
- 593
16
votes
1
answer
2k
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 ...
- 365
12
votes
2
answers
680
views
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 ...
- 14.6k
11
votes
2
answers
459
views
How to derive the effective Hamiltonian of two-dimensional TMDCs monolayers?
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 ...
- 1,733
6
votes
1
answer
65
views
Example of a standard/archetypal/simple 4-band un-gapped condensed matter model with analytic results?
I am looking to study Berry phase-like phenomena in an un-gapped material model. However, I am having trouble finding a widely-used 4-band model with analytic expressions for wavefunctions and ...
- 2,131
5
votes
1
answer
127
views
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 ...
- 125
4
votes
2
answers
210
views
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 ...
- 43
2
votes
1
answer
78
views
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 ...
- 61