Schrodinger equation molecules

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To write the full Schrödinger equation for a mixture of 75% H2 and 25% He, one must first construct the Hamiltonian that accounts for the interactions between all particles, including nuclei and electrons. The Hamiltonian will include Coulomb potentials between pairs of particles, but it does not inherently contain wave-functions or energy terms. The discussion highlights the complexity of solving such equations, noting that exact solutions are typically intractable for multi-particle systems, necessitating approximations like perturbation theory. The participants emphasize the importance of understanding the Hamiltonian's form before delving into approximations, as well as the distinction between the Hamiltonian and the wave-function. Ultimately, the goal is to grasp the foundational equation structure, even if practical solutions remain elusive.
  • #31
So in SI units all I have to do with the kinetic energy term, bracketed T_n, is replace it with this:

- \sum^M_{A=1} ({\frac{h^2 \cdot m_e}{2 \cdot m_A} \cdot \nabla_A^2})

Where m_e is the mass of an electron, m_A is the mass of nucleus A and h (sorry I couldn't find h bar but that's what I meant) is the reduced Planck constant.

And put that into the second Hamiltonian and I would have created a complete SI unit version of the first?
 
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  • #32
Big-Daddy you seem to have some very big misunderstandings. What book have you been studying quantum from?
 
  • #33
I don't study quantum mechanics on its own yet. I have just read the chapters in Atkins' Physical Chemistry.

Is my above expression correct?
 
  • #34
Big-Daddy said:
I don't study quantum mechanics on its own yet. I have just read the chapters in Atkins' Physical Chemistry.

Is my above expression correct?
If it is supposed to be kinetic energy, what are the units on the expression you put forth?

In any event, physical chemistry texts are really horrid on the whole at introducing quantum mechanics. If you want a book that is better, but still chemistry oriented, I'd recommend getting McQuarrie's Quantum Chemistry.
 
  • #35
Sorry, I noticed my answer isn't dimensionally sound. How about this one:

- \sum^M_{A=1} ({\frac{h^2}{2 \cdot m_A} \cdot \nabla_A^2})

I will look into certain books which show some development of more quantum ideas.
 
  • #36
Big-Daddy said:
Sorry, I noticed my answer isn't dimensionally sound. How about this one:

- \sum^M_{A=1} ({\frac{h^2}{2 \cdot m_A} \cdot \nabla_A^2})

I will look into certain books which show some development of more quantum ideas.
Close, it should be hbar but otherwise, so long as M is the number of particles in the system, that is fine.
 
  • #37
Thanks. And is energy (when we solve for it) a function of the position, or a numerical value for the system as a whole?
 
  • #38
Big-Daddy said:
Thanks. And is energy (when we solve for it) a function of the position, or a numerical value for the system as a whole?
It's the latter.
 

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