I need a book to solve Schrodinger's eqn numerically

[jonjacson]

I have found this one that looks perfect:

https://www.amazon.com/dp/331999929X/?tag=pfamazon01-20

THe problem is that it has not been published yet :( , but I can't believe there is no other book on the subject. What I want is to solve numerically the Schrödinger equation with no special techniques, no hartree fock or things like that, I want the whole equation without neglecting anything or aproximating anything.
Do you know any book that explains this and that has been already published?

Thanks

 

[Delta2]

There are many methods for the numerical solving of partial differential equations and specifically of linear PDEs (such as the Schrödinger equation) like the Finite Element Method (FEM) the Finite Difference Method (FDM) and the Finite Volume Method (FVM). Not sure which method is the best for shcrodinger equation, but you could search for books for these methods and see if any book offers special treatment for the Schrödinger equation.

 

[DrClaude]

What I want is to solve numerically the Schrödinger equation with no special techniques, no hartree fock or things like that, I want the whole equation without neglecting anything or aproximating anything.

That's impossible. Simply the fact that computers are digital machines that can only work with a finite set of discrete numbers and a finite number of operations means that you'll have to do some approximations at one point.

There are many different numerical approaches that one can use to solve the Schrödinger equation depending on the situation. What is it exactly you would like to calculate?

 

[jonjacson]

That's impossible. Simply the fact that computers are digital machines that can only work with a finite set of discrete numbers and a finite number of operations means that you'll have to do some approximations at one point.

There are many different numerical approaches that one can use to solve the Schrödinger equation depending on the situation. What is it exactly you would like to calculate?

There is a book from Demtroder that shows spectral data on the elements, I would like to be able to calculate this data, what is the spatial distribution of the electrons on complex atoms etc

 

[jonjacson]

That's impossible. Simply the fact that computers are digital machines that can only work with a finite set of discrete numbers and a finite number of operations means that you'll have to do some approximations at one point.

There are many different numerical approaches that one can use to solve the Schrödinger equation depending on the situation. What is it exactly you would like to calculate?

I know, but I did not mean that.

What I meant is that in the Hartree Fock model you approximate orbitals by spherical shapes, and then you calculate atom properties. I don't want to neglect the fact that real orbitals are not spherical. I hope now you understand what I mean.

 

[jonjacson]

I would welcome more replies, thanks!

 

[DrClaude]

What I meant is that in the Hartree Fock model you approximate orbitals by spherical shapes

This is not what Hartree-Fock is. The basic idea is simply that you transform the multi-electron problem into series of single-electron ones, while considering the potential energy due to the other electrons. There is no requirement for the field created by the other electrons to be spherical. (Note that in the absence of external fields, you expect the total electron distribution to be isotropic.)

I know of an older book, Methods of Molecular Quantum Mechanics by R. McWeeny, that discusses the subject in details (focussing more on molecules than atoms, as the title implies). There may be newer references that are more up to date. You may also look into completely different approaches, such as density functional theory or quantum Monte Carlo. I found the following after a quick search, which may be useful to you: https://arxiv.org/pdf/1008.2369.pdf

 

[jonjacson]

This is not what Hartree-Fock is. The basic idea is simply that you transform the multi-electron problem into series of single-electron ones, while considering the potential energy due to the other electrons. There is no requirement for the field created by the other electrons to be spherical. (Note that in the absence of external fields, you expect the total electron distribution to be isotropic.)

I know of an older book, Methods of Molecular Quantum Mechanics by R. McWeeny, that discusses the subject in details (focussing more on molecules than atoms, as the title implies). There may be newer references that are more up to date. You may also look into completely different approaches, such as density functional theory or quantum Monte Carlo. I found the following after a quick search, which may be useful to you: https://arxiv.org/pdf/1008.2369.pdf

Thanks, I will have a look.