- #1

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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!

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- 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

[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]

Thanks alot! Just one small thing more

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

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

- #5

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thanks again

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