What is the equation for the hypothetical wavefunction with a peak at z=1?

[Ruddiger27]

Sorry, another quick question. If I have a particle confined in a region of space -4 <= Z <=6 where
psi(x)= A(4+z), -4<= z <=1
A(6-z), 1<= z <=6
0 , everywhere else

And I sketch the wavefunction based on the above definitions, what is the actual equation for the wavefunction? The graph gives a peak at z=1 and slopes down to zero either side. Is this supposed to represent a sin(x) function, or am I supposed to just take the above definitions and fit them into the equations for expectation values? I don't think these equations would work in the equation for expectation values.

 

[TMFKAN64]

That *is* the equation for the wavefunction... it is just defined in a piecewise manner. You need to take this definition and put it into the equations for expectation values... but you need to break up the integral into several regions, and put the particular piece of this wave function in. So instead of one integral from negative infinity to positive infinity, you'd have four integrals: negative infinity to -4 (psi is 0), -4 to 1 (psi is A(4+z)), 1 to 6 (psi is A(6-z)) and 6 to infinity (psi is 0 again).

 

[Ruddiger27]

Thanks, that's what I did, but it just seemed a bit wrong to me. Maybe because I thought there was more to it. Anyway, thank you.