Questions tagged [quantum-mechanics]

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

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6
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1answer
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Computational methods for finding the energy eigenvalues of the time-independent Schrodinger equation with arbitrary potential

I have seen in some papers that the energy levels in some arbitrary potential are specified. How can one find the energy levels in such arbitrary potentials. For example, $V(x)=\sin^2(x/2)$ with $x\in[...
34
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6answers
3k views

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 ...
4
votes
1answer
2k views

Partial trace algorithm (original)

In general, is there a partial trace algorithm (ideally for systems of any size) that can be coded using basic matrix operations found in software like Mathematica or Maple? All of the methods I'm ...
12
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1answer
697 views

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 ...
7
votes
1answer
177 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 ...
3
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1answer
410 views

ground state from the Schroedinger equation with a central potential what happens to the origin

I have code that attempts to implement a solution to the Schrödinger equation where there is a central potential (more or less im thinking of hydrogen), in 1-D using the numerov method to construct ...
2
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1answer
2k views

Simple open-source Quantum chemistry or DFT code in C/C++

I know lot of density functional packages in fortran, including one which we are developing in our group (Fireball-DFT) but I don't like fortran very much and I would like something which is easier ...
0
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1answer
1k views

Solving Time dependent Schrodinger equation using MATLAB ode45 [closed]

The Schrodinger equation for time-dependent Hamiltonian is $$i\hbar\frac{d}{dt}\psi(t) = H(t)\psi(t) \, .$$ I try to implement solve the Schrodinger equation for time-dependent Hamiltonian in ODE ...
12
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3answers
3k views

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 ...
3
votes
2answers
290 views

Nanoseconds vs. picoseconds in numerical quantum problems with Matlab ODEs

Hello there and thanks for taking a look at this problem. This problem is related to my previous question and I will therefore use a similar introduction from, Choice of step size using ODEs in ...
2
votes
2answers
559 views

Schrödinger equation with time dependent Hamiltonian

I need to solve the Schrödinger equation with a time dependent Hamiltonian $$i\hbar \frac{\partial}{\partial t} \Psi = \left[-\frac{\hbar^2}{2m}\nabla^2 +\frac{1}{2} k(t)(x^2+y^2) + V(r)\right]\Psi $...
0
votes
1answer
146 views

How to compute matrix representation of $\hat{y}\frac{\partial}{\partial x}$?

I have a 2-dimensional system which I would like to solve numerically (I'm using finite difference method right now), and its an eigenvalue problem. I have a term that looks like $H\psi(x,y) = [-\frac{...