# Constant Wavefunction: Sketch and normalize

The wavefunction of a particle in a box of length $a$ for t = 0 is constant within the range $$\left(\frac{ a}{2}\right) - ϵ$$ and $$\left(\frac{ a}{2}\right) + ϵ$$ and 0 otherwise.

Sketch and normalize this wavefunction.

Where is this particle likely to be found at t = 0?

My question is: is it possible to have a constant wavefunction? The question gives that the wavefunction is constant, but that would mean if you sketch it, it's a horizontal line, and I thought the wave function is always a sinusoidal wave? If it is constant does it still have the formula $$\left(A\sin\frac{ nπx}{a}\right) ?$$ Also if it is constant, isn't it equally likely to be found anywhere within the bounded region at t=0?