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- | Phase factors $e^{i \theta(\vec x,t)}$, like they appear in [[theories:canonical_quantum_mechanics|quantum mechanics]], are just complex numbers with amplitude $1$. Therefore, we can picture them as points on a circle with radius $1$: | + | Phase factors $e^{i \theta(\vec x,t)}$, like they appear in [[theories:quantum_mechanics:canonical|quantum mechanics]], are just complex numbers with amplitude $1$. Therefore, we can picture them as points on a circle with radius $1$: |
The wave function that describes an electron has a specific phase $\Psi(\vec x,t)= |\Psi(\vec x,t)|e^{i \theta(\vec x,t)}$ at each point $\vec x$ at any given moment $t$. Each such phase $\theta$ can be represented by a dot on the unit circle. | The wave function that describes an electron has a specific phase $\Psi(\vec x,t)= |\Psi(\vec x,t)|e^{i \theta(\vec x,t)}$ at each point $\vec x$ at any given moment $t$. Each such phase $\theta$ can be represented by a dot on the unit circle. |