Quantum Wave Function Visualization

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Recommends Roman Odaisky · 2019-10 · Physics Stack Exchange · on “Is there any physical evidence for motion?”

Speaking of wavefunctions, here’s a good visualization: [this video] It shows a complex-valued function of one coordinate, and in 3D it appears to twist around the axis. Roughly, the chirality of that twist shows the direction of the motion and the angular velocity around the axis shows the speed.

Recommends jan0155 · 2020-09 · Physics Stack Exchange · on “How does a sine wave evolve under the Schrodinger equation?”

I would suggest to see this analogy in your book as a visualization of the fact that momentum eigenstates ( $\hat{p}\Psi=\hbar k\Psi$ ) are (infinitely)extended objects in real space and vice versa for the position space eigenstates. Therefore momentum eigenstates can never be eigenstates of the position operator which will lead to the commutator relation used in the uncertaity principle. A time evolution of a unnormalizable mometum state $\sin(kx)$ characterised by the quantum number $k\in\mathbb{R}$ for a free particle Hamiltonian (only kinetic energy) can be done in the following way. $$i\hbar\partial_t\sin(kx)\psi(t)=-\frac{\hbar^2\nabla^2}{2m}\sin(kx)\psi(t)$$ $$i\hbar(\partial_t\psi(t)

Cites NiKS001 · 2020-06 · Physics Stack Exchange · on “Why are wavefunctions in Quantum Mechanics shown as complex Circular waves instead of real Planar waves?”

I'm currently learning Quantum Mechanics from online video lectures and resources. In most of the web articles and videos, the wave functions are shown as circular waves $e^{i\omega t}$ instead of planar waves $\sin{\omega t}$ . [Note: I'm considering a fixed position and hence the equation $e^{i(k\cdot r + \omega t)}$ reduces to $e^{i\omega t}$ ] Some examples from the web: This video shows the wave amplitude to be rotating around the position (i.e. a circular wave in accordance with $e^{i\omega t}$ ): Quantum Wave Function Visualization [this video] The Wikipedia Article on Schrödinger equation describes the plane wave using $e^{i(k\cdot r + \omega t)}$ instead of $\sin{\omega t}$ even though t

Cites NiKS001 · 2020-06 · Physics Stack Exchange · on “Why are wavefunctions in Quantum Mechanics shown as complex Circular waves instead of real Planar waves?”

I'm considering the amplitude at a given position. So you can ignore the $k \cdot r$ . If I understood correctly, $\cos \omega t + i \sin \omega t$ represents a rotating amplitude vector on YZ page with Real component pointing in Y axis and Imaginary component pointing in z axis. (according to the video [this video] ).