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Big-Daddy
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How do I write the non-approximated Schrodinger equation Hamiltonian for a mixture containing 25% by partial pressure of H2 gas and 75% by partial pressure of He gas, at 100 KPa pressure and 298 K?
[itex]p_a[/itex] is the momentum of particle a.Big-Daddy said:What does [itex]p_a[/itex] represent, and don't we have to specify the function [itex]V(\mathbf r_a)[/itex]?
Temperature and pressure are statistical mechanical quantities. I suspect, though one may correct me on this, that pressure can still be reasonably interpreted as the negative derivative of the energy with respect to volume?Big-Daddy said:Shouldn't there be temperature and pressure dependence? Shouldn't there be dependence on how much of each gas is present in the mixture?
Shouldn't there be temperature and pressure dependence? Shouldn't there be dependence on how much of each gas is present in the mixture?
There's no reason to get molecular orbitals if you have the actual wavefunction. MO's are an approximation on the order of hartree fock theory.Big-Daddy said:And can one go directly from a molecular wave-function to the molecular orbital set for that molecule?
Jorriss said:So you're moving out from quantum mechanics then. If you want to know IF they'll react, regardless of the rate, you'd want to compare the free energies. The free energy difference can give the relative proportion of reactants and products.
A Hamiltonian for mixtures is a mathematical representation of the total energy of a mixture of different substances. It takes into account the kinetic and potential energies of each individual component, as well as the interactions between them.
The Hamiltonian for mixtures is different from a regular Hamiltonian in that it includes terms for multiple components, rather than just one. It also takes into account the interactions between components, which a regular Hamiltonian does not.
The Hamiltonian for mixtures is used in various fields of science, such as chemistry, physics, and materials science, to study the behavior of mixtures at a molecular level. It helps researchers understand how different components interact and how this affects the overall properties of the mixture.
Like any mathematical model, the Hamiltonian for mixtures has its limitations. It is based on certain assumptions and simplifications, and may not accurately represent real-world systems. Additionally, it can be complex and difficult to solve, especially for large mixtures.
The Hamiltonian for mixtures is closely related to thermodynamics, as it helps us understand the energy changes that occur in a mixture. By analyzing the Hamiltonian for mixtures, we can determine the equilibrium conditions of a system and make predictions about its behavior under different conditions.