missing minus in intermediate step
File in which the problem appears
2_TDSE_part2.md
Problematic sentence
!!! check "Example:"
What is the expectation value for the kinetic energy $T=\frac{p^2}{2m}$
$$p^2\Rightarrow\frac{\hbar}{i}\frac{\partial}{\partial x}\frac{\hbar}{i}\frac{\partial}{\partial x}=\hbar^2\frac{\partial^2}{\partial x^2}$$
$$\langle T\rangle=\frac{\langle p^2\rangle}{2m}= -\frac{\hbar^2}{2m}\int_{-\infty}^{+\infty} \Psi^* \frac{\partial^2}{\partial x^2} \Psi \mathrm{d}x$$
Note that $p$ is related to the slope of $\Psi$, while $T$ is related to the curvature of $\Psi$!
Correct version
!!! check "Example:"
What is the expectation value for the kinetic energy $T=\frac{p^2}{2m}$
$$p^2\Rightarrow\frac{\hbar}{i}\frac{\partial}{\partial x}\frac{\hbar}{i}\frac{\partial}{\partial x}=-\hbar^2\frac{\partial^2}{\partial x^2}$$
$$\langle T\rangle=\frac{\langle p^2\rangle}{2m}= -\frac{\hbar^2}{2m}\int_{-\infty}^{+\infty} \Psi^* \frac{\partial^2}{\partial x^2} \Psi \mathrm{d}x$$
Note that $p$ is related to the slope of $\Psi$, while $T$ is related to the curvature of $\Psi$!