I'm having some trouble finding an expression for the probability to find the particle outside the classical area in the harmonic oscillator.
I have a wavefunction defined as:
$\psi \left( x,\,t \right)=\frac{1}{2}\left( \sqrt{3}i{{\phi }_{1}}\left( x \right){{e}^{-i{{E}_{1}}t/\hbar }}+{{\phi }_{3}}\left( x \right){{e}^{-i{{E}_{3}}t/\hbar }} \right)$
I'm supposed to give the expression by $P(x,t)$, but not explicitly calculated.
My thought was to use:
${{\int_{a}^{b}{\left| \psi \left( x,t \right) \right|}}^{2}}dx$,
but then I pretty ran into the wall.
So anyone who could give me a hint of what to do ?
Thanks in advance.