By thinking that electrons behave like waves, how does it help to explain that the accelerating particle does not give out energy?
In the ‘solar system’ model of the atom, a particle-like electron travels in a circular orbit around the atom. There are different circles for orbits with different energy. Travelling in a circle, it would be accelerating (centripital acceleration) and so would radiate. In quantum mechanics, the atom has an electron wave. The wave is a bit like a standing wave in a string (see waves and strings), except that it is three dimensional. It is going nowhere. No acceleration, so no radiation. Different energy orbits have different waves, most of them have nodes, just like the waves in a string, except that in three dimensions nodes are surfaces, not points. Now in a string, the wave is in the displacement of the string. What is it that waves in an electron wave? The quantity is called ψ, the Greek letter psi. ψ is a complex quantity it has real an imaginary components. If you take ψ at any place and multiply it by ψ* (which is like ψ, but has the opposite imaginary component, you get the pro
