At t = 0 a particle is in the (normalized) state:(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\Psi(x, 0) = B \sin(\frac{\pi}{2a}x)\cos(\frac{7\pi}{2a}x)[/tex]

With [itex]B = \sqrt{\frac{2}{a}}[/itex]. Show that this can be rewritten in the form [itex] \Psi(x, 0) = c \psi_3(x) + d \psi_4(x)[/itex]

We can rewrite this to:

[tex]\Psi(x, 0) = \frac{B}{2}\left[ c \sin(\frac{4 \pi}{a}x) - d\sin(\frac{3\pi}{a}x)\right][/tex]

The answer sheet gives [itex]c = -d = \frac{1}{\sqrt{2}}[/itex]. I assume you can find this by calculating [itex]A^2 \int \left[ c \sin(\frac{4 \pi}{a}x) - d\sin(\frac{3\pi}{a}x)\right]^2 dx[/itex]. I attempted to do it this way, but it becomes a really long calculation and halfway through I just lose track of everything. Is there an easier way to find c and d?

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Normalizing wave function

**Physics Forums | Science Articles, Homework Help, Discussion**