I tried plugging into the equation t = 3t1/2 and I got A(t) = 0.125A0 since -lambda*t = - ln(2)*t/(t/3) = -ln(2)*3.
So I understand that there will be 12.5% left of the original value since three half-lives have passed.
But then I realized this won't help me answer the question much.
So I'm...
I thought I could start somewhere along the lines of ##\psi(x,t)= \psi(x,0)e^{-iE_nt/\hbar}##, but I'm not sure what ##E_n## would be.
I also thought about doing the steps listed below in the picture, but I'm not sure how to decompose ##\psi(x,0)## like it says to in the first step.
Any help...
I know that ahat_+ = 1/sqrt((2*m*h_bar*w)) * (mw(xhat)+i(phat)) and ahat_- = 1/sqrt((2*m*h_bar*w)) * (mw(xhat)-i(phat)). But I'm not sure what (ahat_+)^+ could be.
I was planning to find the value of N by taking the integral of φ*(x)φ(x)dx from -∞ to ∞ = 1. However, this wave function doesn't have a complex number so I'm not sure what φ*(x) is. I was thinking φ*(x) is exactly the same φ(x), but with x+x0 instead of x-x0.
Thank you