Now, it follows from Equation ([e3.54]) that \[H \equiv -\frac{\hbar^{\,2}}{2\,m}\,\frac{\partial^{\,2}}{\partial x^{\,2}} + V(x).\] However, according to Schrödinger’s equation, ([e3.1]), we have \[-...Now, it follows from Equation ([e3.54]) that \[H \equiv -\frac{\hbar^{\,2}}{2\,m}\,\frac{\partial^{\,2}}{\partial x^{\,2}} + V(x).\] However, according to Schrödinger’s equation, ([e3.1]), we have \[-\frac{\hbar^{\,2}}{2\,m}\,\frac{\partial^{\,2}}{\partial x^{\,2}} + V(x) = {\rm i}\,\hbar\,\frac{\partial}{\partial t},\] so \[H \equiv {\rm i}\,\hbar\,\frac{\partial}{\partial t}.\] Thus, the time-dependent Schrödinger equation can be written \[\label{etimed} {\rm i}\,\hbar\,\frac{\partial\psi}{\p…