Different forms of Schrodinger equation

QMechanic · Aug 21, 2014

I got confused when in my book they went from one form of Schrödinger equation to another. It doesn't make much sense to me algebraically, probably i have some lacks in complex numbers. Here are the equations:

Time-dependent Schrödinger equation printed in a textbook: i ħ ∂Ψ/∂t = −(ħ²/2m) ∂²Ψ/∂x² + VΨ.

Printed textbook page showing d/dt of the integral from minus infinity to plus infinity of |Psi(x,t)|^2 dx equal to the integral of the partial derivative with respect to t of |Psi|^2 dx, then the product rule for the partial derivative of |Psi|^2 and the time-dependent Schrodinger equation for partial Psi / partial t.

In the second one I think it's implied that above two equations give third and I am not sure how.

mfb · Aug 21, 2014

The last equation of the second picture is the same as the equation in the other picture, just multiplied by ##\frac{-i}{\hbar}## (note that -i * i = 1)

QMechanic · Aug 21, 2014

Thanks I completely forgot about it haha

Different forms of Schrodinger equation

Discussion

Similar threads