Schrodingers equation probability currents

[golfingboy]

Hi all,

I only have a real basic knowledge of quantum mechanics and I am finding a paper that I am taking quite challenging. If it is possible for someone to give me a hint or starting point on this folowing problem that would be great.

For problem - see attachment

Thanks.

 

[Physics Monkey]

I would start by writing $$\rho = |\psi|^2 = \psi^* \psi$$ and differentiating with respect to time. You will get two pieces from the product rule. Try using Schrödinger's equation on each piece to write the time derivatives in terms of spatial derivatives. Hint: you may find it useful to take the complex conjugate of the Schrödinger equation.

 

[Gokul43201]

Hi all,

I only have a real basic knowledge of quantum mechanics and I am finding a paper that I am taking quite challenging. If it is possible for someone to give me a hint or starting point on this folowing problem that would be great.

For problem - see attachment

Thanks.

Golfingboy,

we typically require that you show some effort on your part before we can help you. Please read the guidelines or the sticky thread at the top of this sub-forum.

As for your question, it looks like there's a typo in the first line, involving the integration variable (unless P is something other than the density).

Thirdly, I hope you've come across the continuity equation in fluid mechanics or in E&M. The question loses it's zing value if the solver can not appreciate the coneection to the above.