Looking for help on Lancsoz algorithm to solve schrodinger equ

In summary, the Lanczos algorithm is a numerical method used for solving eigenvalue problems, particularly in quantum mechanics. It works by reducing a large symmetric matrix into a smaller tridiagonal matrix through a series of orthogonal transformations. Its advantages include efficiency, stability, and accuracy, but it may not be suitable for all types of matrices. It can be implemented using various software packages or by writing custom code with a strong understanding of linear algebra and numerical methods.
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Dear frnds,
if we take an hydrogen atom and we wish to find out the PD function of 1st, 2nd and 3rd orbital. please help me finding out some doc on it.
 
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  • #2
Which 2nd and 3rd orbital?

Go to this link. If it doesn't scroll you to the right portion you are looking for section on Wavefunction. Specifically, equation for ψ. Notice n, l, and m. These are the 3 quantum numbers describing an orbital.

PD is given by ψ multiplied by its own complex conjugate.
 

1. What is the Lanczos algorithm?

The Lanczos algorithm is a numerical method used to solve eigenvalue problems, particularly the Schrodinger equation in quantum mechanics. It is based on the Lanczos process, which is a method for reducing a large symmetric matrix into a smaller tridiagonal matrix.

2. How does the Lanczos algorithm work?

The Lanczos algorithm works by approximating the eigenvalues and eigenvectors of a matrix through a series of orthogonal transformations. These transformations are computed using a three-term recursion relation, which results in a tridiagonal matrix that is easier to solve for eigenvalues and eigenvectors than the original matrix.

3. What are the advantages of using the Lanczos algorithm?

One advantage of the Lanczos algorithm is its efficiency in solving large eigenvalue problems. It is also known for its stability and accuracy, making it a popular choice for solving problems in quantum mechanics and other areas of physics.

4. Are there any limitations to the Lanczos algorithm?

While the Lanczos algorithm is useful for many types of problems, it is not suitable for all types of matrices. It works best for symmetric matrices, and may not be as effective for non-symmetric or non-Hermitian matrices.

5. How can I implement the Lanczos algorithm in my research?

There are various software packages and libraries available that implement the Lanczos algorithm. Some popular options include ARPACK, LAPACK, and SciPy. It is also possible to write your own code to implement the algorithm, but this may require a strong understanding of linear algebra and numerical methods.

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