Why representing particle in box by single wavelength not by wave packet physics dtack exchange?
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Here is what I have gathered so far:
Particles like an electron (i.e. with rest mass) can be represented as matter waves (deBroglie).
The matter wave of a particle can be modelled a wave packet.
A wave packet Ψ(r⃗ ,t)Ψ(r→,t) is a superposition of plane waves. A distinctive feature of a plane wave is the wave vector k⃗ k→, which points into the direction into which the plane is propagating. Citing Wikipedia: Ψ(r⃗ ,t)=a⋅∫k⃗ A(k⃗ )ei(k⃗ r⃗ −ωt)d3p⃗ Ψ(r→,t)=a⋅∫k→A(k→)ei(k→r→−ωt)d3p→
So far, I think I am mostly accurate. But now, here is what I am not so sure about
A wave packet for a free particle has spherical symmetry. I always envisage a hairy ball, hard at the core, getting softer to the outside, where hardness stands for the amplitude of the wave packet.
For an (infinite) bunch of planes waves to superpose into a spherical symmetry, not all k⃗ k→ of the component plane waves may point into the same direction.
Particles like an electron (i.e. with rest mass) can be represented as matter waves (deBroglie).
The matter wave of a particle can be modelled a wave packet.
A wave packet Ψ(r⃗ ,t)Ψ(r→,t) is a superposition of plane waves. A distinctive feature of a plane wave is the wave vector k⃗ k→, which points into the direction into which the plane is propagating. Citing Wikipedia: Ψ(r⃗ ,t)=a⋅∫k⃗ A(k⃗ )ei(k⃗ r⃗ −ωt)d3p⃗ Ψ(r→,t)=a⋅∫k→A(k→)ei(k→r→−ωt)d3p→
So far, I think I am mostly accurate. But now, here is what I am not so sure about
A wave packet for a free particle has spherical symmetry. I always envisage a hairy ball, hard at the core, getting softer to the outside, where hardness stands for the amplitude of the wave packet.
For an (infinite) bunch of planes waves to superpose into a spherical symmetry, not all k⃗ k→ of the component plane waves may point into the same direction.
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