In: Chemistry
using the time independent SWE Htsi=Etsi.
what does it mean when they say the SWE is solved numerically and the wave function is improved by successive numerical iterations.
and what is the main use for the SWE. (in atoms)
is the main solution energy or tsi
Schrödingers wave equation(time independent) is given as:
Where, = Hamiltonian
E = energy of the wavefunction
= wave function.
Now obtaining a wave function exactly which describes an atom or a particle with many elctrons neutrons is impossible to achieve because of my types of interactions present which cannot be solved numerically. Sowe take a trial wave function and try to achieve the observable E. Now it is acceptable if the energy is deviating too much from the actual energy. So we now improve the wave function by adding some terms to it and keeping the boudary conditions intact and again try achieving the energy value by putting in the Schrödinger equation. Repeating this process will bring the energy closer and closer to the actually measured energy from reliable instruments. This is called variational principal and is the most easiest way to achieve to the energy Eigen value, E, and can be done by simple algorithms.
Vaiational principal:
where is a normalised wave equation.