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1) Let the state of a quantum particle be represented by \(\displaystyle \phi\). Show that if \(\displaystyle \phi\) satisfies Schrodinger's equation, then its norm is constant.

2) Now consider a quantum particle with state \(\displaystyle \phi_{t}\) defined on [-a,a] subject to potential V=0.

State the differential equation that \(\displaystyle \phi_{t}\) solves in terms of partial derivatives of x and t.