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Natural sciences course of the University of Cambridge

Year of the natural sciences course of the University of Cambridge

Year 4 of the natural sciences course of the University of Cambridge

Physics course of the year 4 of the natural sciences course of the University of Cambridge

Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge

2012

Paper 1

Section A

<Wavefunction normalization> cancels in the ratio of integrals:
$$
\boxed{P(a/2<x<a)=\frac{\int_{a/2}^a(a^2+x^2)dx}{\int_0^a(a^2+x^2)dx}
=\frac{19a^3/24}{4a^3/3}=\frac{19}{32}.}
$$
A normalized version of the specified <wavefunction> is $\sqrt3(a+ix)/(2a^{3/2})$ on its support.

Solution

Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / Section A / A1 / b / Solution

Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge / 2012 / Paper 1 / Section A / A1 / b / Solution

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