Sovling schrodinger's equation in C++

[Rasine]

i need help coming up with a way to solve for the eigen vectors of schrodinger's time independant equation in c++.

so i want to write a class that uses the shooting method, but i am not sure how to do that.

 

[tm1729]

try these methods
http://pagesperso-orange.fr/jean-pierre.moreau/c_eqdiff.html

 

[quicknote]

I can understand the importance of solving Schrodinger's equation in various fields of physics and engineering. Using C++ to solve this equation can be a challenging task, but it is definitely possible.

To solve for the eigen vectors of Schrodinger's time independent equation, you can use the shooting method. This method involves solving an initial value problem by breaking it down into smaller boundary value problems. In C++, you can write a class that implements the shooting method by defining functions for the initial value problem, boundary value problem, and the shooting algorithm itself.

Firstly, you can define a function for the initial value problem, which takes in the initial conditions of the wave function and its derivative. This function can be solved using a numerical integration method like the Runge-Kutta method.

Next, you can define a function for the boundary value problem, which takes in the boundary conditions of the wave function. This function can be solved using the initial value problem function and a root-finding algorithm like the bisection method.

Finally, you can implement the shooting algorithm by using the initial value problem and boundary value problem functions to iteratively adjust the initial conditions until the boundary conditions are satisfied. This will give you the eigen vectors of Schrodinger's equation.

Additionally, you can also consider using existing libraries or packages in C++ that are specifically designed for solving differential equations like Eigen or Armadillo. These libraries provide efficient and accurate methods for solving Schrodinger's equation.

In conclusion, solving Schrodinger's equation in C++ using the shooting method can be achieved by defining appropriate functions and implementing the shooting algorithm. With careful implementation and use of libraries, you can obtain accurate results for the eigen vectors of Schrodinger's equation.