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ShayanJ

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Imagine you go to his mother and ask whether she knows where her son is. She looks at the clock and says the school is finished ten minutes ago and so he should be on the way. But where? She can't tell you where her son is, only where he is probably. So she brings a map and marks different regions where she thinks the boy may be in. Those regions are called orbitals.

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bhobba

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No.

They are solutions to Schroedinger's equation.

The why of Schroedingers equation is actually quite deep, involving some tricky advanced math - if you are interested you will find it in Chapter 3 of Ballentine - Quantum Mechanics - A Modern Development:

https://www.amazon.com/dp/9810241054/?tag=pfamazon01-20&tag=pfamazon01-20

Believe it or not its the principle of relativity - the POR.

Thanks

Bill

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One then talks of

Here is a nice site that allows you to visualize the atomic orbitals of hydrogen.

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jtbell

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Mathematically, the hydrogen atom “orbitals” (energy-eigenstate solutions of the Schrödinger equation) are very similar to standing waves of e.g. sound in a spherical cavity.

For standing waves of sound in a spherical cavity, the microscopic displacement of an air molecule at location ##(r,\theta,\phi)## as it oscillates has the form

$$f(r,\theta,\phi,t) = R_n(r)Y_{lm}(\theta,\phi) \cos (\omega t)$$

where ##\omega = 2 \pi f## and n, l, m are integers which label different forms of the R and Y functions.

The hydrogen orbitals have the form

$$\Psi(r,\theta,\phi,t) = R_n(r)Y_{lm}(\theta,\phi) e^{i \omega t}

= R_n(r)Y_{lm}(\theta,\phi) \left[ \cos (\omega t) + i \sin (\omega t) \right]$$

where ##\omega = 2 \pi f = 2 \pi E / h = E/\hbar## and again n, l, m are again labels which we usually call “quantum numbers.”

The R functions are different for the two situations, because the boundary conditions are different. The sound waves do not penetrate beyond the wall of the spherical cavity, but there is no "wall" that sets a fixed boundary to the hydrogen ψ function.

However, the Y functions are exactly the same: the well-known and well-studied "spherical harmonic" functions.

And the sound waves oscillate in time according to a real cosine function, whereas the hydrogen ψ oscillates according to a complex ##e^{i\omega t}##.

As you probably know, the complex "square" ##|\Psi|^2 = \Psi^*\Psi## gives you the relative probability of finding the electron in a particular location ##(r,\theta,\phi)## at time t,

If you

Questions like "Do electrons

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But what is physics?

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