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Why is the momentum operator imaginary? The simplest explanation hinges on the fact that observables are represented by Hermitian operators in quantum mechanics. Once we accept this, then we can show that the momentum operator $\hat{p} = -\mathrm{i}\hbar\nabla$ is Hermitian precisely because of the factor of $\mathrm{i}$. We need to show that for any two ...


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Because periodic waves can be represented using exponential functions using imaginary arguments I'm going to attempt a non-rigorous explanation that might give some intuition as to why imaginary numbers appear in the mathematics of quantum stuff. Most of this doesn't require a knowledge of what a Hermitian operator is or about vector spaces or eigenvalues. ...


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The simplest approximation you can make is to describe each orbital by a one-electron wavefunction like the ones we find in the hydrogen atom. For those wavefunctions, the radial distribution is described by an exponential factor of $exp(-Zr/n)$ (with $n$ the principal quantum number) and a polynomial with mixed powers of $Z$ and $r$. If you increase $Z$, ...


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