Sign Issue with Zitelli Quantum Mechanics 3.6

[katieranthony]

Homework Statement

A particle of mass m, in an infinite potential well of length a, has the following initial wave function at t = 0:

Relevant Equations

probability current density vector and partial time derivative of p

I will include a photo. Essentially, we need to prove that dp/dt + the gradient of J(x,t) = 0.
We are getting that the two are instead equal and opposite, and have checked with multiple people.

 

[katieranthony]

Homework Statement: A particle of mass m, in an infinite potential well of length a, has the following initial wave function at t = 0:
Relevant Equations: probability current density vector and partial time derivative of p

I will include a photo. Essentially, we need to prove that dp/dt + the gradient of J(x,t) = 0.
We are getting that the two are instead equal and opposite, and have checked with multiple people.

 

[katieranthony]

 

[katieranthony]

View attachment 340359

 

[katieranthony]

Here is our work. Please let us know if you have any suggestions! We are genuinely very curious.

 

[kuruman]

Here is our work. Please let us know if you have any suggestions! We are genuinely very curious.

Your work in the photo is illegible. It would be best if you used LaTeX. When you do so, maybe you will resolve the negative sign problem. It's probably some silly mistake that you keep repeating because you are convinced that it's correct (it has happened to me too). Start fresh and don't copy from the board.

 

[hutchphd]

Homework Statement: A particle of mass m, in an infinite potential well of length a, has the following initial wave function at t = 0:
Relevant Equations: probability current density vector and partial time derivative of p

We are getting that the two are instead equal and opposite, and have checked with multiple people.

What two things are equal and opposite?? If $x_1$ and$~x_2$ are equal and opposite , don't they sum to zero?? I am confused.