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 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.
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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 ...
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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 ...
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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 ...
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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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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 ...
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What does āstrongly correlatedā mean?

For quantum many body problem, there is a common terminology āstrong correlated systemsā that appears in different context. However, it seems that the definition of it is ambiguous and sometimes ...
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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 ...
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What is the best program to manipulate plane-wave 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 ...
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First order variation of the wave function of conduction states

The first order variation of the wave function $\Delta \psi_n$ is obtained by standard perturbation theory (Eq. 25 of ref 1): (H_{SCF}-\epsilon_n)|\Delta \psi_n \rangle = -(\Delta V_{...
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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 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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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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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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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 is the error in a wavefunction related to the error in energy?

While studying the variational method in McQuarrie's Quantum Chemistry, I came across the following problem: to relate the difference between an approximation $\phi$ and the exact ground-state wave ...
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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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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 ...
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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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