Visualizing the beauty in physics and mathematics
⭐ Idea taken from the book Visualizing Quantum Mechanics with Python
📌 Ported to from VPython to JavaScript and Three.js
🔧 Source code in 2d_infinite_square_well_3d.js
👉 vertical cylinders represent the complex value of the wavefunctio
👉 height $\propto$ to the real part of the wavefunction
👉 radius $\propto$ to the imaginary part
👉 the color represents the value of the phase factor
👉 the systems evolves by summing the Fourier coefficients times the eigenstate
A 2D Infinite Square Well (ISW) is a potential well that has zero potential energy over a finite domain in two directions, say the $x$- and $y$-directions, and is infinite outside that domain. The simplest case is a rectangular domain in the $xy$-plane with sides $L_x$ and $L_y$. In this case the 2D time-independent Schrödinger wave equation factors into two 1D time-independent Schrödinger wave equations, one in the $x$-direction and one in the $y$-direction. The wavefunction is then a product of the two 1D wavefunctions. The wavefunction is then given by a superposition of energy eigenstate wavefunctions of the form $\psi_{nm}(x, y) = A \sin(n\pi x/L_x) \sin(n\pi y/L_y )$. — Visualizing Quantum Mechanics with Python
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