Linked Questions

0
votes
2answers
3k views

Eigenvalue problem and plotting its eigenfunctions [duplicate]

How many different ways can one solve an eigenvalue problem and plot its corresponding eigenfunctions in Mathematica? For example for Harmonic Oscillator? Which one is the most accurate one? Thanks ...
521
votes
19answers
129k views

Where can I find examples of good Mathematica programming practice?

I consider myself a pretty good Mathematica programmer, but I'm always looking out for ways to either improve my way of doing things in Mathematica, or to see if there's something nifty that I haven't ...
26
votes
1answer
3k views

How to numerically solve a 1-d time-independent Schrödinger equation?

The point is to solve the eigensystem of the given Hamiltonian. I tried ParametricNDSolve combined with FindRoot to search for ...
11
votes
1answer
2k views

Schrödinger eigenvalue problem in two dimensions (Harmonic Oscillator)

I read here the discussion about how to solve a one-dimensional eigenvalue problem. I am wondering, how can one generalize these methods to two dimensions? For example, how to solve this equation: $$...
3
votes
2answers
356 views

How to numerically solve the Schrödinger equation for Lennard-Jones potential?

Hi I have a potential like below: V[x_]:= 102*(4343/x^12 - 650/x^6) + 33/x^2 Which is a kind of modified Lennard-Jones potential. Schrödinger equation is 1D ...
11
votes
1answer
517 views

How to add AccuracyGoal and PrecisionGoal options in a numerical function?

There are many built-in functions that contain AccuracyGoal, PrecisionGoal and ...
3
votes
3answers
318 views

General function for the expansion of a polynomial of operators

This question is motivated by a Quantum mechanical problem - but in explaining the problem - I assume no knowledge of quantum mechanics. I want to define a function that can expand and simplify the ...
3
votes
4answers
709 views

Hypergeometric function with a matrix argument

I am looking for the evaluation of a Hypergeometric function with a matrix argument as for example in Koev and Edelman or as showcased in this Wikipedia article. From what I understand from ...
5
votes
1answer
584 views

How to find the roots of an equation which is almost singular everywhere

I'm trying to find the roots of the equation as a variable of k: ...
4
votes
1answer
250 views

Solving the eigenvalue problem for a double well potential using a 1D particle in a box as a basis set

My first question is how would I go about getting the 1D particle in a box eigenfunctions using matrix techniques and how would I use the particle in a box eigenfunctions as a basis set for the ...
1
vote
1answer
844 views

Numerical solution of Schrödinger equation

I want to solve the following differential equation numerically. The geometry of the problem is as shown below. Electron 1 is located on the inner ring of radius $R_1$ and electron 2 is located on the ...
1
vote
1answer
156 views

ParametricNDSolveValue for ODE with boundary at infinity

I'm trying solve the Schrödinger equation for a given potential using the function ParametricNDSolveValue following the the first method of the post: Find eigen energies of time-independent Schrö...
3
votes
0answers
115 views

Stationary 1-D Schrodinger equation for calculating energy of a -CH3 group quantum rotor in a metal organic framework

I am trying to calculate the energy of a quantum mechanical rotor by plugging a potential function predicted from DFT calculations in this paper: DOI:10.1039/C8CC02650E The potential can be ...