Can the Schrödinger equation be solved analytically?

There are few potentials for which the Schrödinger equation can be solved explicitly for all nr radial and l orbital quantum states. However, analytic solutions are possible only for a few simple quantum systems like the movement in the spherical simmetrical field and the linear harmonic oscillator [1, 3, 4, 5].

Why is the Schrödinger equation impossible?

The potential energy function can only be written as above: a function of all the spatial positions of each particle. Unfortunately, the Coulomb repulsion terms make it impossible to find an exact solution to the Schrödinger equation for many-electron atoms and molecules even if there are only two electrons.

Why can the Schrödinger equation be solved analytically for hydrogen but not for Helium?

You can solve the Schrödinger equation for the hydrogen atom exactly however for larger atoms you can’t solve the equations exactly, you can only use approximations. My professors have always said exact solutions for atoms such Helium can’t be obtained because “the math is too complicated”.

Why does it become difficult to mathematically describe the coulombic interactions in a Multielectron atom?

Why does it become difficult to mathematically describe the Coulombic interactions in a multi-electron atom? Heinseberg’s uncertainty principle makes it impossible to determine the exact location of the electrons. For multi-electron atoms, no two electrons are allowed an identical set of four quantum numbers.

What do you get when you solve the Schrödinger equation?

The Schrödinger equation is a linear partial differential equation that governs the wave function of a quantum-mechanical system. The Schrödinger equation gives the evolution over time of a wave function, the quantum-mechanical characterization of an isolated physical system.

What are the limitations of Schrödinger wave equation?

To sum up, the Schrodinger equations’ weaknesses include: Not describing spin. Not transforming properly under the motion of the observer. Not handling relativity, causing answers to be inaccurate.

How did Schrödinger create his equation?

In their paper, the physicists developed a new way to obtain the Schrödinger equation starting from a mathematical identity using classical statistical mechanics based on the Hamilton-Jacobi equation. In quantum mechanics, both amplitude and phase depend on each other, and this makes the quantum wave equation linear.”

Can Schrodinger’s equation be solved for atoms with more than one electron?

Schrodinger’s equation cannot be solved exactly for atoms with more than one electron because of the repulsion potential between electrons. You can find more about that in any quantum chemistry textbook.

What is the first step in Schrodinger’s equation?

First step – a hydrogen atom” http://vixra.org/pdf/1306.0014v1.pdf , http://www.slideshare.net/alexanderilyanok/femtotechnologies-step-i-atom-hydrogen-alexander-ilyanok Schrodinger’s equation cannot be solved exactly for atoms with more than one electron because of the repulsion potential between electrons.

Why is the electron configuration problem so difficult to solve?

The problem for atoms with more than one electron is that the equation describes many body wavefunctions. That’s the main difficulty. These days it can be solved using pseudopectral methods, though, of course, bound states require special care.

How accurate is Schroedinger’s equation for helium?

It is true that Schroedinger’s equation cannot be solved *exactly* for many-electron systems. However, for small atoms, there are incredibly accurate numerical methods, essentially based on the variational principle. Thus for Helium the results are comparable to experimental precision.