# Questions tagged [quantum-mechanics]

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

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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: $$\left[-\frac{\hbar^2}{2m}\frac{d^2}{dr^2}+V(r)+\frac{\hbar^2l(l+1)}{2mr^2}\right]R(r)=ER(r).$$ ...
52 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 ...
112 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 ...
149 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/...
40 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?
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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): ...
90 views

### Numerical solution to the infinite well problem

I've used the following code to implement it ...
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### Ising model in Python (Magnetization Scaling)

I am trying to implement the Ising Model in Python for Gibbs Distribution: $$\pi(x) = \frac{1}{Z(\beta)} e^{-\beta H(x)}$$ \begin{align*} p(x,y)&=r(x,y) \cdot \min \left( \frac{\pi(y)}{\pi(x)},1 \...
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### Problems with the time-dependent Schrödinger equation solutions

I have this Mathematica problem that solves numerically the time-dependent Schrödinger equation in a box: ...
246 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 ...
84 views

### 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. ...
582 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 ...
193 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 ...
380 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: $$\frac{1}{x^2}\frac{d}{dx}\left(Gam \frac{dL}{dx}\right)+L\left(\frac{a^2x^2}{Gam}-m^2\right)=0$$ ...
343 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 ...
153 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 ...
256 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 ...
62 views

### Is there a software package for Quantum Monte Carlo estimation of the exchange correlation functional?

Quantum Monte Carlo (QMC) calculations historically have been used to parameterise the exchange-correlation functionals for Density Functional Theory (DFT). For example, this article explains a way to ...
4k views

### Solving the 1D Particle-in-a-Box using C++

I've just finished learning the physics behind the problem and would like to write a program in C++ than can solve the problem. I'm actually stuck at the start. I've quite a bit of research, the ...
830 views

### Numerical propagation of a density matrix using Liouville von Neumann equation

I want to look at time evolution of the density matrices of some, very simple, spin systems, but I am having trouble with my approach. I want to use a simple for-...