Schrodinger equation of a free particle in the rectilinear

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Schrodinger equation of a free particle in the rectilinear


With the wave function in the laboratory reference already known, relate the wave functions of the initial and new references via phase factors, and represent the time and spatial derivatives of the initial wave function with those of the wave function in new reference. Through adjusting the phase factor, conclusions are drawn that when the rectilinear reference frame moves uniformly to the laboratory reference, the form of Schrodinger equation remains unchanged; yet if the rectilinear reference is under uniform acceleration, the Schrodinger equation (and its Hamiltonian) will add an energy dimensional term equivalent to a static potential field towards the opposite direction of the acceleration. In the end extensions of the conclusions are put forward.
 
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