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Year 2 of the mathematics and philosophy course of the University of Oxford

Options I for mathematics and philosophy course of the University of Oxford

Past exam of the options I for mathematics and philosophy course of the University of Oxford

2013

The <Time-dependent Schrödinger equation> is
$$
\boxed{i\hbar\partial_t\Psi=-\frac{\hbar^2}{2m}\partial_x^2\Psi+V(x)\Psi.}
$$
A <stationary state> of <energy> $E$ has a <wavefunction> $\Psi(x,t)=\psi(x)e^{-iEt/\hbar}$, where
$$
-\frac{\hbar^2}{2m}\psi''+V\psi=E\psi.
$$
Its time dependence is only a <global phase>, and its <probability density> is independent of time.

Solution

Past exam of the options I for mathematics and philosophy course of the University of Oxford / 2013 / J / 1 / a / Solution

Past exam of the options I for mathematics and philosophy course of the University of Oxford / 2013 / J / 1 / a / Solution

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Past exam of the options I for mathematics and philosophy course of the University of Oxford / 2013 / J / 1 / a / Solution

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