General form of the Schrödinger equation for one particle in 1D ↩

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created: 2021-12-11 13:25:23
modified: 2022-01-11 18:35:58

The Hamiltonian operator is usually expressed as the sum of two operators corresponding to the kinetic and potential energies of a system:

Where the potential energy is generalized

Where is the position.
And for a particle moving in , the kinetic energy is:

Where is the momentum operator and is the mass of the particle, is the nabla operator.

The Hamiltonian operator takes the form:

So the Schrödinger equation of the system is: