- #1
Petraa
- 21
- 0
Hello,
I've been spending a lot of time trying to solve this problem but I can't figure out a good solution.
I have to show that the action of a non-relativistic particle ( Schrodinger density Lagrangian ) is invariant under Galilean boost with the form
ψ(x0,x)→ψ'(x0,x)=eimvx-(im/2)x0v2ψ(x0,x-vx0)
x0= t
I've tried to find the transformed Lagrangian by replacing the wave functions and the derivatives but I'm not sure I did it correctly because I get monstrous expressions
I'm using this density Lagrangian L= ihψ*[itex]\partial[/itex]0ψ+h2/2m([itex]\partial[/itex]iψ*)([itex]\partial[/itex]iψ)
If someone can give me a good tip I'll appreciate it
thank you!
I've been spending a lot of time trying to solve this problem but I can't figure out a good solution.
I have to show that the action of a non-relativistic particle ( Schrodinger density Lagrangian ) is invariant under Galilean boost with the form
ψ(x0,x)→ψ'(x0,x)=eimvx-(im/2)x0v2ψ(x0,x-vx0)
x0= t
I've tried to find the transformed Lagrangian by replacing the wave functions and the derivatives but I'm not sure I did it correctly because I get monstrous expressions
I'm using this density Lagrangian L= ihψ*[itex]\partial[/itex]0ψ+h2/2m([itex]\partial[/itex]iψ*)([itex]\partial[/itex]iψ)
If someone can give me a good tip I'll appreciate it
thank you!