Integral of Psi*Psi needs to be finite (square integrable). You can have a function go to zero as r->inf. that would not be square integrable.DEvens said:The usual thing is to have the wave function go to zero as radius goes to infinity. Is that enough?
Quantum Defect said:Integral of Psi*Psi needs to be finite (square integrable). You can have a function go to zero as r->inf. that would not be square integrable.
And you can have square integrable functions which don't go to 0 when their argument goes to infinity.Quantum Defect said:Integral of Psi*Psi needs to be finite (square integrable). You can have a function go to zero as r->inf. that would not be square integrable.
The Schrodinger equation is a mathematical equation that describes the behavior of quantum systems, such as atoms and molecules. It was developed by physicist Erwin Schrodinger in 1926 and is a cornerstone of quantum mechanics.
Boundary conditions refer to the specific conditions that must be satisfied at the boundaries of a system in order for a solution to the Schrodinger equation to be valid. These conditions are necessary for determining the energy levels and wave functions of a quantum system.
Boundary conditions are crucial in the Schrodinger equation because they determine the allowed energy levels and wave functions of a quantum system. Without satisfying these conditions, the solution to the equation would not accurately describe the behavior of the system.
Some common boundary conditions for the hydrogen Schrodinger equation include the normalization condition, which ensures that the wave function is properly normalized, and the boundary condition at the origin, which ensures that the wave function is continuous at the origin.
Boundary conditions play a crucial role in determining the solutions to the hydrogen Schrodinger equation. They restrict the possible energy levels and wave functions for a hydrogen atom, leading to the quantization of energy levels in an atom.