# Questions tagged [quantum-mechanics]

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

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### How to get a Wannier function of tight-binding model numerically (i.e. Python)

I have a question on construction of a Wannier function for tight-binding model. Let's say we consider the tight-binding model of 1D chain with two atoms( site A and B in a unit cell). In k-space we ...
1 vote
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### Solving the non-linear Hamiltonian using Scipy's root finding method

I am a complete novice to computational physics and am finding difficulty in implementing a code to iteratively solve for a $2\times2$ nonlinear Hamiltonian using Scipy's root solver. I can't seem to ...
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1 vote
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### Roothaan equations and Galerkin method

When we do Hartree-Fock computations by solving the Roothaan equations $FC = SC \varepsilon$ is it a Galerkin method?
1 vote
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### Numerical Solution of the Schrödinger equation for hydrogen

I'm trying to solve the Schrödinger equation for the hydrogen atom in the following form numerically: $$\left[-\frac{\hbar^2}{2m}\frac{d^2}{dr^2}+V(r)+\frac{\hbar^2l(l+1)}{2mr^2}\right]R(r)=ER(r).$$ ...
62 views

### Numerov method for 1D potential barrier problem: numerical errors

I wanted to solve a 1D potential barrier problem. It seemed easy enough to do: set a travelling wave coming from the left, part of it gets reflected by the barrier, and part of it gets gets ...
130 views

### Computing eigenvalues of Schrodinger equation with spin

I want to solve a 2-dimensional particle in box problem with two electrons in the quantum well.I would like to take into account spin of electrons and Coulomb interactions to compute singlet and ...
1 vote
228 views

### How to compute the Eigenvalue and Eigenstates of Quantum well with Effective mass using finite difference method in Python?

I want to compute the eigenvalues and eigenstates of a quantum well with different effective masses of electron in the barrier and in the quantum well. As can be seen : https://github.com/mholtrop/...
43 views

### Numerically solving schrodinger equation [duplicate]

Consider the potential given above: $$U(r) = \frac{U_0}{\exp[(r - r_0)/\epsilon] + 1}\, .$$ How to solve the Schrodinger equation with this potential numerically and find the eigenvalues?
1 vote
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### Weird behavior in for solving TISE in harmonic oscillator potential using the shooting method

I was solving the time independent Schrödinger equation using the shooting method for harmonic oscillator potential. This is the code that I wrote for that with the results (code is written in julia): ...
1 vote
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### Numerical solution to the infinite well problem

I've used the following code to implement it ...
79 views

### Problems with the time-dependent Schrödinger equation solutions

I have this Mathematica problem that solves numerically the time-dependent Schrödinger equation in a box: ...
373 views

### Numerov method for solving Schrödinger equation

I have just begun learning computer science to apply it to Physics and I am trying to write a code for solving Schrödinger's equation of the harmonic oscillator (setting $V=\frac{x^2}{2}$) in one ...
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### Finding the extrema of a transition probability function for a quantum walker on a graph

The goal Implement some Python code to find the extrema points of a function that is strongly oscillating. The background Let $G$ be a connected graph with $n$ points with Laplacian matrix $L(G)$. We ...
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### Python routine to calculate shape resonances of H2

I am currently doing a project in which my aim is to write a program that can be used to calculate single and multi-channel shape resonances. So I'm looking at bound states and quasi-bound states. ...
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### Numerov method for Schrodinger equation

While learning about numerical methods for solving the Schrödinger equation I came across Numerov's method. I want to get the solution for the harmonic oscillator by alreading giving the eigenvalues. ...
1 vote
598 views

### What will be the impact of quantum computing on existing numerical techniques (e.g. CFD)?

Quantum computing seems to be a very active and promising development area in computer science. However, I am curious as to what impact (if any) quantum computing will have on existing classical ...
1 vote
240 views

### How to do Weierstrass-transform in MATLAB?

I have a diagonalization problem. I have the eigenstates correctly, and I want to do a Gaussian-smearing (Weierstrass-transform) on them. So I have the wave functions ($\Psi$), and the continuous ...
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### Magnetization Vector from XY Model for an AntiFerromagnetic System

I am working on an XY model and I'm trying to calculate the magnetization and direction for an anti-ferromagnetic (AF) system. So I have a collection of spins in the $XY$ plane represented as vectors ...
404 views

### Avoiding divergent solutions with odeint? shooting method

I am trying to solve an equation in Python. Basically what I want to do is to solve the equation: $$\frac{1}{x^2}\frac{d}{dx}\left(Gam \frac{dL}{dx}\right)+L\left(\frac{a^2x^2}{Gam}-m^2\right)=0$$ ...
357 views

### Matrix exponential of hermitian matrix with eigenvectors from generalized eigenvalue problem

I want to calculate the following expression $$\exp(-i\Delta t\mathbf{H})$$ where $\mathbf{H}\in\mathbb{C}^{n\times n}$ is a hermitian matrix. Since I have a highly optimized eigensolver in the code ...
159 views

### Two variables integration matlab

I'm trying to solve physical problem in quantum mechanics of helium atoms, the solution require numerical integration over 2 variables. However when i'm trying to run the next code ...
276 views

### 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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### Normalizing a density matrix at each iteration

I need to numerically evolve a density matrix using this formula(Actually I have more terms but right nows I am starting with this and facing problems): $$\dot\rho(t) = -i[H(t), \rho(t)]$$ $H(t)$ is ...
1 vote