Brian Shotwell
University of California, San Diego
Department of Physics
Quantum Mechanics Primer Desmos Plots
To view any of the following, copy-paste into Desmos.com.
The Sawtooth Wavefunction Psi_{saw}(x) with n terms included:
Change "5" in the upper limit of the sum to other numbers:
\left\{x<0:0,x>1:0,\sum_{n=1}^{5}(-1)^{n-1}\cdot \frac{\sqrt{12}}{\pi\ n}\sin\left(n\cdot\pi\cdot x\right)\right\}
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Probability Density |Psi_S(x)|^2 over time:
Set the slider "t" to go from 0 to 1, and have the step size be 0.01 or 0.001.
\left\{x<0:0,x>1:0,\sin\left(\pi\cdot x\right)\cdot \sin\left(\pi\cdot x\right)+ 2\cdot\sin\left(\pi\cdot x\right)\cdot \sin\left(2\cdot\pi\cdot x\right)\cdot \cos\left(2\cdot\pi\cdot t\right)+ \sin\left(2\pi\cdot x\right)\cdot \sin\left(2\pi\cdot x\right)\right\}
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Probability Density |Psi_{saw}^{(n<=5)}(x)|^2 over time:
Set the slider "t" to go from 0 to 1, and have the step size be 0.01 or 0.001.
\left\{x<0:0,x>1:0,\frac{12\sin^2(2\pi t)\sin^2(\pi x)}{\pi^2}+\frac{3\sin^2(8\pi t)\sin^2(2\pi x)}{\pi^2}+\frac{4\sin^2(18\pi t)\sin^2(3\pi x)}{3\pi^2}+\frac{3\sin^2(32\pi t)\sin^2(4\pi x)}{4\pi^2}+\frac{12\sin^2(50\pi t)\sin^2(5\pi x)}{25\pi^2}+\frac{8\sin(2\pi t)\sin(18\pi t)\sin(3\pi x)\sin(\pi x)}{\pi^2}+\frac{24\sin(2\pi t)\sin(50\pi t)\sin(5\pi x)\sin(\pi x)}{5\pi^2}-\frac{12\sin(2\pi t)\sin(8\pi t)\sin(2\pi x)\sin(\pi x)}{\pi^2}-\frac{6\sin(2\pi t)\sin(32\pi t)\sin(4\pi x)\sin(\pi x)}{\pi^2}+\frac{3\sin(8\pi t)\sin(32\pi t)\sin(2\pi x)\sin(4\pi x)}{\pi^2}+\frac{8\sin(18\pi t)\sin(50\pi t)\sin(3\pi x)\sin(5\pi x)}{5\pi^2}-\frac{4\sin(8\pi t)\sin(18\pi t)\sin(2\pi x)\sin(3\pi x)}{\pi^2}-\frac{2\sin(18\pi t)\sin(32\pi t)\sin(3\pi x)\sin(4\pi x)}{\pi^2}-\frac{12\sin(8\pi t)\sin(50\pi t)\sin(2\pi x)\sin(5\pi x)}{5\pi^2}-\frac{6\sin(32\pi t)\sin(50\pi t)\sin(4\pi x)\sin(5\pi x)}{5\pi^2}+\frac{12\cos^2(2\pi t)\sin^2(\pi x)}{\pi^2}+\frac{3\cos^2(8\pi t)\sin^2(2\pi x)}{\pi^2}+\frac{4\cos^2(18\pi t)\sin^2(3\pi x)}{3\pi^2}+\frac{3\cos^2(32\pi t)\sin^2(4\pi x)}{4\pi^2}+\frac{12\cos^2(50\pi t)\sin^2(5\pi x)}{25\pi^2}+\frac{8\cos(2\pi t)\cos(18\pi t)\sin(3\pi x)\sin(\pi x)}{\pi^2}+\frac{24\cos(2\pi t)\cos(50\pi t)\sin(5\pi x)\sin(\pi x)}{5\pi^2}-\frac{12\cos(2\pi t)\cos(8\pi t)\sin(2\pi x)\sin(\pi x)}{\pi^2}-\frac{6\cos(2\pi t)\cos(32\pi t)\sin(4\pi x)\sin(\pi x)}{\pi^2}+\frac{3\cos(8\pi t)\cos(32\pi t)\sin(2\pi x)\sin(4\pi x)}{\pi^2}+\frac{8\cos(18\pi t)\cos(50\pi t)\sin(3\pi x)\sin(5\pi x)}{5\pi^2}-\frac{4\cos(8\pi t)\cos(18\pi t)\sin(2\pi x)\sin(3\pi x)}{\pi^2}-\frac{2\cos(18\pi t)\cos(32\pi t)\sin(3\pi x)\sin(4\pi x)}{\pi^2}-\frac{12\cos(8\pi t)\cos(50\pi t)\sin(2\pi x)\sin(5\pi x)}{5\pi^2}-\frac{6\cos(32\pi t)\cos(50\pi t)\sin(4\pi x)\sin(5\pi x)}{5\pi^2}\right\}
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