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This is about how the Schrodinger equation applies to a free particle. Imagine an electron floating in space, never encountering anything, so there is effectively no potential. In the time-independent Schrodinger equation, the Hamiltonian operator is applied to the wavefunction, representing the total energy with kinetic energy (momentum squared divided by twice the mass) and potential energy (V of X) components. The particle is in one-dimensional space, not three-dimensional.
