there's the equation and the difference between the time dependent and time independent is that in the dependent \hat H is a linear operator acting on the wavefunction Ψ. \hat H takes as input one Ψ and produces another in a linear way, a function-space version of a matrix multiplying a vector and in the independent the exponentially growing solutions have an infinite norm, and are not physical. They are not allowed in a finite volume with periodic or fixed boundary conditions.




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