- #1

- 83

- 0

I'm trying to find the relation between the lagrangian density and the hamiltonian, does anyone know how they are related? I also need a reference where I can find the relation.

Thanks!

- Thread starter kaksmet
- Start date

- #1

- 83

- 0

I'm trying to find the relation between the lagrangian density and the hamiltonian, does anyone know how they are related? I also need a reference where I can find the relation.

Thanks!

- #2

- 410

- 0

[tex]\mathcal{H} = \pi \dot{\phi} - \mathcal{L}[/tex],

where

[tex]\pi = \frac{\partial\mathcal{L}} { \partial ( \partial_t \phi ) }[/tex]

The Hamiltonian is then

[tex]\int\!d^3x\, \mathcal{H}[/tex]

- #3

- 83

- 0

Thanks alot! Just one small thing more

[tex]\mathcal{H} = \pi \dot{\phi} - \mathcal{L}[/tex],

where

[tex]\pi = \frac{\partial\mathcal{L}} { \partial ( \partial_t \phi ) }[/tex]

The Hamiltonian is then

[tex]\int\!d^3x\, \mathcal{H}[/tex]

If the Hamiltonian is [tex]\int\!d^3x\, \mathcal{H}[/tex], then what is [tex]\mathcal{H}[/tex]? And is [tex]\mathcal{L}[/tex] the lagranian or the lagranian density?

Last edited:

- #4

- 410

- 0

The integral over [tex]\mathcal{H}[/tex] is the Hamiltonian, and the integral over [tex]\mathcal{L}[/tex] is called the Lagrangian.

- #5

- 83

- 0

thanks again

- Last Post

- Replies
- 1

- Views
- 429

- Last Post

- Replies
- 30

- Views
- 6K

- Last Post

- Replies
- 13

- Views
- 6K

- Replies
- 1

- Views
- 807

- Replies
- 18

- Views
- 6K

- Last Post

- Replies
- 3

- Views
- 4K

- Replies
- 3

- Views
- 2K

- Last Post

- Replies
- 13

- Views
- 4K

- Replies
- 3

- Views
- 2K

- Replies
- 21

- Views
- 3K