Schrödinger equation in 1D ↩

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created: 2021-12-22 19:00:48
modified: 2022-01-19 16:54:09

Let's consider the simplest case for a moving particle in QM: the particle moves in 1D, so in the space.

In this case the position operator is just simply multiplication with :

And the momentum operator is:

Since the usual classical Hamiltonian is where is the potential, we can reasonably take the following Hamiltonian operator:

Then we can just substitute this into the Schrödinger equation: