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When we talk about light waves or EM waves, we simply say that the wave packet is the superposition of other waves of different wavelengths. In quantum mechanics, we say the same thing; the superposition of many waves associated with electron form a wave packet. I don't understand this, because one wave is associated with one electron. It is only superimposed with other electron waves. Does an electron make superpositions with itself having different wavelengths? How is this possible?

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    $\begingroup$ It's not really clear what you're asking imo, wavefunctions can always be written as a linear combination of other wavefunctions because there always exists an orthonormal eigenbasis corresponding to each Hermitian operator (i.e. observable). This is what is meant by "superposition". $\endgroup$
    – Charlie
    Commented May 21, 2021 at 17:07

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Bcs one wave is associated with one electron.

This is not true! You should rather say, There is a unique wave function $|\Psi(t)\rangle$ (or In position basis $\psi(x,t)$) associated with a particular state of system.

There is something very nice about $|\Psi(t)\rangle$ but not very new, If $|\psi\rangle$ and $|\psi'\rangle$ represent the possible wave function of the electron then so does the $\alpha |\psi\rangle+\beta |\psi'\rangle$. That's called the Principle of Superposition.

A wave packet is a simple superposition of different wave forms,

$$\psi(x,t)=\frac{1}{\sqrt{2\pi}}\int \phi(k)e^{i(kx-\omega t)}dk$$

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The state of a particle is given by the wave function (state vector $\psi$), which we get by solving the Schrödinger's equation. This wave function can be written as the superposition of many other simpler wave functions analogous to Fourier decomposition. Hence, the superposition of those simpler wave functions gives the overall wave function of a single electron.

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