A finite wave train propagating along the positive x-axis with a constant speed v must satisfy the normal wave equation rather than the Schrödinger equation. The normal wave equation maintains the shape of the wave function f(x-vt), while the Schrödinger equation, which involves both second derivatives in space and first derivatives in time, alters the shape of the wave. The discussion clarifies that the Schrödinger equation functions more as a dispersion equation due to its first-order time derivative, contrasting with the characteristics of the normal wave equation.
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You have the same derivates in the normal wave equation.pam said:The normal wave train. The shape of f(x-vt) is unchanged in the wave equation.
Since the Schrödinger equation involves d^2/dx^2 and d/dt, the shape will change.
Yes, it's true.pam said:The normal wave equation has d^2/dt^2.