# Questions tagged [quantum-mechanics]

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

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### Will hashing become vulnerable to quantum computers?

My knowledge of these subjects is reasonable but limited so please correct anything I say that is wrong. As I understand a hash, with today's technology, is virtually irreversible. Also, any good hash ...
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### Solving the time dependent Schrödinger equation with leapfrog integration in 1D

To my frustration I am struggling to implement leapfrog integration for the time dependent Schrödinger equation. To the best of my knowledge this was first explicitly done in "A fast explicit ...
177 views

### 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: $$\left[-\frac{\hbar^2}{2m}\frac{d^2}{dr^2}+V(r)+\frac{\hbar^2l(l+1)}{2mr^2}\right]R(r)=ER(r).$$ ...
91 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 ...
160 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
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### 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/...
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 ...
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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: ...
544 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. ...
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### 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
339 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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### MATLAB: Faber approximation of the matrix exponential to solve Liouville-von-Neumann equation

EDIT: I moved the full code to my github page so the post can be read more easily. I am writing a script to take the Faber approximation approach outlined in Hassan Fahs paper (free access) and apply ...
606 views

### Incorporating a potential barrier in a wave-packet simulation (Fourier Transform method)

I'm trying to simulate the scattering of a wave-packet at a potential barrier in Python. I'm using a Fourier Transform method (not sure if its the same as the Split-Step method), where I apply Fourier ...
1 vote