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Quantum Mechanics Series Lecture 4Lecture 1 established that ρ(x,t) = |ψ(x,t)|² behaves like a conserved probability density. Lecture 2 showed what drives that flow. We also saw that writing ψ = r exp(iθ) makes the probability current proportional to the phase gradient, making it clear that phase geometry literally steers the motion. Lecture 3 then showed that the centroid of that flow can move almost classically when the packet is tight and the external potential is smooth.However, that raises
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Quantum Mechanics Series Lecture 4Lecture 1 established that ρ(x,t) = |ψ(x,t)|² behaves like a conserved probability density. Lecture 2 showed what drives that flow. We also saw that writing ψ = r exp(iθ) makes the probability current proportional to the phase gradient, making it clear that phase geometry literally steers the motion. Lecture 3 then showed that the centroid of that flow can move almost classically when the packet is tight and the external potential is smooth.However, that raises
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The Wavefunction Learns the Shape of a BarrierA Quantum wavepacket moves across a two-dimensional plane and meets a smooth potential island. The surface is the computed probability density |ψ(x,y,t)|², while the colour comes from the phase arg ψ. The ripples, transmitted lobes, reflected interference, and tunneling leakage all come directly from the Schrödinger equation.#QuantumScattering #PotentialBarrier #ProbabilityDensity #WavefunctionPhase #QuantumTunneling #SchrodingerEquation
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The Wavefunction Learns the Shape of a BarrierA Quantum wavepacket moves across a two-dimensional plane and meets a smooth potential island. The surface is the computed probability density |ψ(x,y,t)|², while the colour comes from the phase arg ψ. The ripples, transmitted lobes, reflected interference, and tunneling leakage all come directly from the Schrödinger equation.#QuantumScattering #PotentialBarrier #ProbabilityDensity #WavefunctionPhase #QuantumTunneling #SchrodingerEquation
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