Quantum Mechanics in Coordinate and Moment Representations Through Three Simple Problems
Abstract
In this paper we present the solution of the stationary Schrödinger equation in the coordinates and momentum
representations for three simple problems: the linear potential, the harmonic oscillator and the Dirac delta
potential. We verify through explicit calculation that the wave functions obtained in each representation
are connected through the Fourier transform, showing that both solutions constitute two complementary
representations of the same quantum state. From a pedagogical point of view, this shows that both solutions
contain information of equal theoretical value and constitute two complementary representations.
Keywords
Schrödinger equation, coordinates and momentum representations, Fourier transform.
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