- #1
jfy4
- 649
- 3
Hi,
I am wondering if all the old collisions problems from beginning physics can still be applied and solved for using quantum mechanics. For example. In mechanics we used conservation of momentum and kinetic energy in elastic collisions to solve for out-going momentums of pool balls. Can the same techniques be used for say, electron-electron scattering (non-relativistic)?
Say I have two particles, thing one and thing two. Can I use this system of equations to solve for the out-going momentums
[tex]\frac{\partial \psi(x_1)}{\partial x_1}+\frac{\partial\psi(x_2)}{\partial x_2}=\frac{\partial\psi'(x_1)}{\partial x_1}+\frac{\partial\psi'(x_2)}{\partial x_2}[/tex]
and
[tex]\frac{\partial^2\psi(x_1)}{\partial x_1^2}+\frac{\partial^2\psi(x_2)}{\partial x_2^2}=\frac{\partial^2\psi'(x_1)}{\partial x_1^2}+\frac{\partial^2\psi'(x_2)}{\partial x_2^2}.[/tex]
Which I think are the 1D analogues for elastic collisions between pool balls. I would need to specify directions and signs too. But say I know the in-coming momentums, can I use these to solve for the out-going momentums?
I am wondering if all the old collisions problems from beginning physics can still be applied and solved for using quantum mechanics. For example. In mechanics we used conservation of momentum and kinetic energy in elastic collisions to solve for out-going momentums of pool balls. Can the same techniques be used for say, electron-electron scattering (non-relativistic)?
Say I have two particles, thing one and thing two. Can I use this system of equations to solve for the out-going momentums
[tex]\frac{\partial \psi(x_1)}{\partial x_1}+\frac{\partial\psi(x_2)}{\partial x_2}=\frac{\partial\psi'(x_1)}{\partial x_1}+\frac{\partial\psi'(x_2)}{\partial x_2}[/tex]
and
[tex]\frac{\partial^2\psi(x_1)}{\partial x_1^2}+\frac{\partial^2\psi(x_2)}{\partial x_2^2}=\frac{\partial^2\psi'(x_1)}{\partial x_1^2}+\frac{\partial^2\psi'(x_2)}{\partial x_2^2}.[/tex]
Which I think are the 1D analogues for elastic collisions between pool balls. I would need to specify directions and signs too. But say I know the in-coming momentums, can I use these to solve for the out-going momentums?