Time Independent Schrodinger Equation

[mrojc]

Homework Statement

Verify that a plane wave ψ(x) = Ae^-ikx is a solution to the time independent Schrödinger equation for a free particle in one dimension. Can it be normalised? Why?[/B]

Homework Equations

The Attempt at a Solution

My lecturer's notes are all over the place, which is frustrating. The only notes that I seem to have on this question, I cannot understand because they're scattered. If anyone has a link to a proof, or notes on it, I would be so grateful.

 

[Ken G]

Just look up the equation, and plug in that solution, and show it works. Then notice that the solution is infinite in space, with constant magnitude (it is a complex number of magnitude |A|² but a phase that varies in space and time), so it cannot be normalized to unity when integrated over all space.