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The Hamiltonian is included in this equations, which contains the Kinetic energy operator. When Schrodinger wrote thi he converted momentum to the unit imaginary number, the reduced Planck constant and the Delta operator.

My question is that this means that the Kinetic energy will be the same regardless of the characteristics of the quantum level particle. This does not make sense, surely the kinetic energy will affect the evolution of the state, due to the fact that it is energy.

Thanks to whoever clears this up for me.

-H