Question

Can someone please explain to me Schrodinger's wave theory of the atomic structure to me please.. >< I am struggling to understand it.

Answer 1

Think of the waves you can make in a bathtub if you slosh the water with your hand. Only certain waves are stable, if you watch carefully. One in which the water sloshes back and forth with it reaching a max on one side of the tub when it's a min on the other side, and then, if you slosh faster, another in which the water is at min or max at both ends with a peak (or trough) in the middle, and then another still faster. You'll see the same thing if you wiggle a rope tied to a pole, or if you pluck a violin or guitar string. Only waves that "fit" exactly into the length of string are stable and continue to vibrate for a while.

So this tells you why wave disturbances in a confined medium (the water in a tub, or a string tied between two posts) are "quantized," meaning they can only have certain frequencies (or equivalently wavelengths or energies of vibration).

The only remaining question is how and why an electron in an atom should be described by a wave confined within the atom. The "how" is easy: we imagine a weird sort of imaginary wave called a "wavefunction" confined with the electron, and calculate its properties. (It's weird because it can be complex, i.e. have real and imaginary components, among other things.) Once we do, we can calculate properties of the electron by calculating the inner product of various operators with the wavefunction. The easiest thing to calculate would be the probability density of finding the electron at any position, which would just involve multiplying the wavefunction by its complex conjugate at that point. (We can then find the probability of finding the electron within any given distnance by adding up, integrating, the probability density over that volume.)

The "why" is much harder. Why on Earth should this procedure work? Why should the properties of the electron be given by such a strange procedure? That is a profoundly difficult question to answer, and really hasn't been fully satisfactorily answered yet. I will suggest two possibilities which are studied: (1) the basic nature of matter *is* continuous, i.e. there are no such thing as "electrons," just some underlying "electron field" that fills all space, and various contortions and complex vibrations of this field can appear, to our crude senses, as "particles." (2) particles have the ability to interact with each other over any distance essentially instantaneously in a way we do not yet understand -- meaning we don't yet understand the limitations on how they can interact -- and it just turns out the way in which they interact can be understood as if they were both "attached" in some sense to an imaginary wave.

Answer 2

Thank you for your help :3