Dynamics of the Wave Function: Heisenberg, Schrödinger, Collapse


What does Schrödinger equation say?
Hummm… That’s a tough one. I have a lot of trouble making sense out of it. Here’s the best explanation I’ve come up with. At any position of space, a wave function has a particular energy which is deduced from its global structure. This local energy, also known as the Hamiltonian, is a composition of some potential energy which is due to external forces like electromagnetism, and some kinetic energy which depends on the superposition of momenta which makes up the wave function. What’s particularly weird about this kinetic energy is that it can have a complex value. Now, what Schrödinger equation says is that, at every position, the wave function rotates around the origin of the complex plane at a speed proportional to the Hamiltonian. This corresponds to the following formula:

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