In quantum mechanics, in the 'particle in a box' topic, I studied that by solving the Schrödinger equation, we can actually find out what the wave function of the particle in a box looks like. Corresponding to different energy levels, the particle can have different wave functions. For e.g., in it's ground state (lowest energy level), the wave function looks like a standing wave (with nodes at the edges of the box) if we just look at the real part of the wave function. But in reality if we look at the entire wave function (including the imaginary part), it's wave function is actually a wave that is rotating through the real and the imaginary planes. There are plenty of animations in YouTube regarding this.
Similarly, what does the wave function of an electron look like? In my book, no description has been given as to what the wave function of an electron looks like. I mean what does the plot of $Ψ(r,θ,\phi,t)$ (since we use spherical polar coordinates while solving the Schrödinger equation for an atom; $t$ is time) look like?
I don't want to just see the time-independent components of the wave function. I want to see what the wavefunction look like if we let time run (for e.g., for a particle in a box, the wave function just looks like a static wave but when we let time run, the wave function is actually a wave rotating through the real and imaginary planes). Can someone please show me a plot or animation of $Ψ(r,θ,\phi,t)$ so that I can visualise what the wave function of an electron looks like? For instance, what does the wave function of the electron in, say, a hydrogen $1s$ orbital look like? Similarly, what does the wave function of electrons in other orbitals look like?