Recent content by gabriellelee

That was a typo. I meant t=(t1/2)/3

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...

$$\hat{S_+} = \hbar \begin{bmatrix} 0 & \sqrt{2} & 0 \\ 0 & 0 & \sqrt{2} \\ 0 & 0 & 0 \end{bmatrix}$$ $$\hat{S_-} = \hbar \begin{bmatrix} 0 & 0 & 0 \\ \sqrt{2} & 0 & 0 \\ 0 & \sqrt{2} & 0 \end{bmatrix}$$ $$\hat{S_x} = \hbar/\sqrt{2} \begin{bmatrix} 0 & 1 & 0 \\ 1 & 0 & 1 \\ 0 & 1 & 0...

I know intuitively that the integral is 1, can you explain it to me mathematically?

1?

-∞ to +∞

Are the right two terms ##\psi(x)## and the first term is ##C_n##?

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

Is it saying is the plane in the xy or xz or yz plane?

Oh, okay. Thank you so much!

I still don't get why only the first ##\hat r## is replaced with ##\hat z## and same for m for the second one.

This is what I got.