Can the Schrödinger equation be solved exactly?

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.

Is the Schrödinger equation difficult?

Analytic solutions are harder to obtain, because the Schrödinger equation is a second order partial differential equation in variables (3 coordinates for each of particles and one time variable) with variable coefficients. That makes it challenging to solve even in the most trivial cases.

Is Schrödinger equation in JEE?

Schrodinger wave equation or just Schrodinger equation is one of the most fundamental equations of quantum physics and an important topic for JEE.

What is the solution to Schrödinger’s wave equation?

The wave function Ψ(x, t) = Aei(kx−ωt) represents a valid solution to the Schrödinger equation. The wave function is referred to as the free wave function as it represents a particle experiencing zero net force (constant V ).

Can Schrödinger equation be solved for helium?

The Schrödinger equation was solved very accurately for helium atom and its isoelectronic ions (Z=1–10) with the free iterative complement interaction (ICI) method followed by the variational principle. We obtained highly accurate wave functions and energies of helium atom and its isoelectronic ions.

Which function will be normalized if?

A normalized wave function ϕ(x) would be said to be normalized if ∫|ϕ(x)|2=1. If it is not 1 and is instead equal to some other constant, we incorporate that constant into the wave function to normalize it and scale the probability to 1 again.

What does solution of Schrödinger equation gives?

Given a set of known initial conditions, Newton’s second law makes a mathematical prediction as to what path a given physical system will take over time. The Schrödinger equation gives the evolution over time of a wave function, the quantum-mechanical characterization of an isolated physical system.