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2.) what is mean by <x|[itex]\psi[/itex]>? is it mean x(position) mean the final state we reach where we extract form |[itex]\psi[/itex]> ? from eigen value equation [itex]\hat{x}[/itex] |[itex]\psi[/itex]>=[itex]\lambda[/itex]|[itex]\psi[/itex]> where [itex]\lambda[/itex] is the eigen value of position. so why do we need <x|[itex]\psi[/itex]>?