# Questions tagged [quantum-mechanics]

Numerical methods and problems involving the solution of the Schrodinger equation and related subatomic models.

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### Are there simple ways to numerically solve the time-dependent Schrödinger equation?

I would like to run some simple simulations of scattering of wavepackets off of simple potentials in one dimension. Are there simple ways to numerically solve the one-dimensional TDSE for a single ...
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### Where do the laws of quantum mechanics break down in simulations?

As someone who holds a BA in physics I was somewhat scandalized when I began working with molecular simulations. It was a bit of a shock to discover that even the most detailed and computationally ...
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### Choice of step size using ODEs in matlab

Hey there and thanks for giving time to look at my question. This is a updated version of my question which I posted earlier in physics.stackexchange.com I'm currently studying a 2D exciton spinor ...
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### Numerical Methods for the Schrodinger Equation

We are comparing the performance of various numerical methods that can be used to solve the Schrodinger's Equation for the Hydrogen Atom interacting with a strong laser pulse (too strong to use ...
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### What is the current state of the art in solving higher dimensional parabolic PDEs (multi-electron Schrödinger equation)

What is the current state of the art for solving higher dimensional (3-10) parabolic PDEs in the complex domain with simple poles (of the form $\frac{1}{|\vec{r}_1 - \vec{r}_2|}$) and absorbing ...
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### Why is it difficult to numerically solve multi-electron time-dependent Schrödinger's equation

It seems that people usually use the Single Active Electron (SAE) approximation to deal with a multi-electron system, transforming the problem into a single electron problem. For example, in ...
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### Confusion about Quantum Monte Carlo

My question is about extracting observables from QMC methods, as described in this reference. I understand the formal derivation of various QMC methods like Path Integral Monte Carlo. However, at the ...
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### How to find Lyapunov exponent for coupled system

Answer gives a software for calculating conditional Lyapunov exponent (CLE) for coupled oscillators in chaos synchronization. However, it is hard to follow and there is no graphical output of the ...
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### Forcing an ODE solver to preserve the norm

I have an ODE of the form $$\frac{dy}{dt} = -i H y \enspace .$$ where $y$ is a complex vector and $H$ is a time dependent Hermitian matrix. The norm of the solution $y(t)$ at any point in time ...
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### Non-hermitian discretizations in quantum mechanics

Consider the Schroedinger equation $$\left(-\frac12\frac{\partial^2}{\partial x^2} + V(x) \right) \psi(x) = E \psi(x)$$ The usual way to solve it is to introduce a discretization of $\psi(x)$. This ...
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### Why do QM programs use redundant internal coordinates for geometry optimization?

Brief explanation of QM geometry optimization Quantum mechanics packages are often tasked with optimizing a chemical structure. The problem is essentially this: Given a set of points in 3D space and ...
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### Split operator FFT quantum dynamics for a harmonic oscillator

I would like to do a numerical quantum dynamics of a displaced gaussian in harmonic oscillator using split-operator method (see bottom of these notes by Hal Evans for the algorithm). I have a problem ...
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### Monte Carlo normalization of a wave function

I would like to normalize a quantum mechanical multi-particle wave function numerically, and since the result is a multidimensional integral I thought Monte Carlo methods might be appropriate. So, I'm ...
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### Implementation of the Numerov Method for the 1D square well

I want to solve the Schrodinger via the Numerov Method but I had some troubles. I'm programing in C++, so here is my code: ...
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### A programming model for Quantum Mechanics angular momenta in Mathematica

I'm writing prototypes for solving the Liouville Equations with Mathematica and C++. Perhaps the question about this may not be suited for this forum in a strict way, but it suits the people here ...
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### Trying to generate a wave function basis set

For a little project I'm working on, I am trying to generate a wavefunction basis set I can use in Quantum Monte Carlo (DMC to be specific). Preferably, it would be a linear combination of Slater ...
### Numerical integration of SDE: choice of $dt$ and algorithm
I am working on the following Stochastic Differential Equation (SDE) in the Quantum Mechanics context: $$dX_{t} = a X_{t} dt + b X_{t} dW$$ where $X_{t}$ is my stochastic varible, $dt$ is my ...