Hamiltonian of a human

[luc]

I possess varius textbooks about QM, and in them they always show the Hamiltonian of simple things, like electrons or harmonic oscillators, but I wonder which is the hamiltonian of a more complex thing, for example a human body

[Tom Mattson]

You would write down the Hamiltonian for all the atoms in the body.

 

Now for the real question: Why on Earth would you want to?

[Johnny5]

You would write down the Hamiltonian for all the atoms in the body.

 

Now for the real question: Why on Earth would you want to?

 

Tom what exactly is the Hamiltonian. I've tried several times to learn Lagrangian Dynamics' date=' and I know that the Hamiltonian can be written in terms of the Lagrangian, but I cannot seem to remember either, well we'll see in a moment I will check. I think the main reason I haven't learned is because I can't see the utility. One of the authors started out by discussing holonomic and non-holonomic constraints, and sceleromic(sp?) and non sceleromic constraints. And lost me, and then this same author also discussed degrees of freedom, and I didn't quite follow that either.

 

Another thing that bugged me, is that this same author said that it is believed that both Lagrangian, and Hamiltonian approach to dynamics are equivalent to Newtonian Dynamics, but the author wasn't certain. That was a bit well didn't make me want to keep reading.

 

Let me see if I even remember the Lagrangian. I don't think I will get this right, and I'm not gonna google for the answer.

 

Let E denote total energy of a system.

 

Let U denote potential energy, let T denote kinetic energy.

 

E = T + U

 

The Lagrangian I think is umm

 

L = T - U

 

Maybe?

 

I'm gonna leave that as my first guess, and now I'll google.

 

Ok, here is Wolfram on the Lagrangian.

 

Yeah ok, so I remembered it, but I cannot think of any instance where I would use it.

 

Thanks

[□h=-16πT]

For a system whose motion is conservative the Hamiltonian gives the total energy of the system. The importance of the Hamiltonian is that it allows one to demonstrate any conservation laws for the system. For example a conservative system has (follows from Hamilton's equations and the "total derivative") dH/dt=0 and so H=constant, i.e. the total energy of the system is conserved. Noether's (sp?) theorem states that for every coordinate the Hamiltonian is independant of there exists a conservation law for it (or at least to give the theorem roughly). From Hamilton's equation one may also derive the equations of motion for the system.

[luc]

You would write down the Hamiltonian for all the atoms in the body.

 

Now for the real question: Why on Earth would you want to?

 

 

Mmm, to know the wavefunction of a human body for example?

I think that can be interesting if someday quantum teleportation of a human body is tried

[Tom Mattson]

Mmm' date=' to know the wavefunction of a human body for example?

I think that can be interesting if someday quantum teleportation of a human body is tried[/quote']

 

This would be an impossible task in practice. First you would have to know the exact configuration of every single atom in the human body. Second you would have to know the state of each of those atoms at some particular instant. And then the hard part starts! Solving the Schrodinger equation for a 3 body problem (eg: a Helium atom) is not possible to do exactly; an approximation must be used. To calculate the wavefunction of an object the size of a human to any acceptable degree would require more computing power than is available in the whole world, to put it mildly.