# Time Evolution of a Quantum Free Particle in 2D

Time Evolution of a Quantum Free Particle in 2D

This Demonstration shows the time evolution and dispersion relation for a 2D quantum free particle represented by , where ,(x,y)= and ,=+ are the eigenfunctions and energy levels, respectively, for . The left graphic shows the complex wavefunction , where the shape is its modulus and the coloring is according to its argument, the range to corresponding to colors from red to magenta. The right panel shows a surface plot of the 2D quadratic dispersion relation, .

ψ(x,y,t)=,(x,y)

ϕ

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-,t/ℏ

E

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e

ϕ

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1

2π

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e

1

2π

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2

ℏ

2

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2

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2m

-∞<,<∞

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ψ(x,y,t)

0

2π

ω(,)=,ℏ

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E

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