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Numerical Solution of the Hydrogen Atom

Shodor > CSERD > Resources > Courses > Numerical Solution of the Hydrogen Atom

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The Hydrogen Atom

This module presents the problem of determining the most likely position, or orbital, of an electron around a hydrogen atom. The mechanics of quantum particles are determined by a partial differential equation known as Schrodinger's wave equation. This sets up an eigenvalue problem that limits the possible energies of the electron. The computational solution of Schrodinger's equation for hydrogen i typically done via separation of variables, in which the radial solution is separated from the angular solution, in effect reducing the problem to 1 dimension and allowing for standard numerical integration techniques to be applied.

The angular solution of Schrodinger's equation for the hydrogen atom can be expressed in terms of the spherical harmonics. Once the solution is obtained, a variety of computational techniques can be used to visualize the orbitals for different energies.

The importance of matching the types of boundary conditions to the problem will be demonstrated in the module, as well as limitations of the numerical techniques used.

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