Variational method For Helium Atom

In summary, when using the variational method for the Helium atom, it is determined that the lowest possible energy occurs when 1<z<2, where z is the atomic number. This is because there is a probability that the electron may be very close to one of the protons, making it seem as if there are only two protons. However, it is not possible for z to be between 0 and 1, as this would mean the effective nuclear charge seen by an electron is smaller than 1, which is not possible. Additionally, even if both electrons were located inside the nucleus, it would still be possible to distinguish them based on the concept of effective nuclear charge.
  • #1
Bishop556
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When using the variational method for the Helium atom, we determine that the lowest possible energy occurs when 1<z<2 where z is the atomic number. My professor elaborated that the number is within this range because there is a probability that the electron may be so close to one of the protons that it appears as if there are only two protons. My question is why can't 0<z<1? Why can't both electrons be located inside the nucleus of the atom? Would it still be possible to distinguish them if they were?
 
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  • #2
I suppose z is the effective nuclear charge seen by an electron, ie the nuclear charge scrreened by the other electron. This can t be smaller than 1.
 

What is the variational method for Helium Atom?

The variational method is a mathematical technique used to approximate the ground state energy of a system, such as the Helium atom, by optimizing a trial wavefunction. It is based on the principle that the true ground state energy is always lower than any approximate energy calculated using a trial wavefunction.

Why is the variational method useful for Helium Atom?

The variational method is useful for Helium Atom because it allows for a more accurate calculation of the ground state energy compared to other approximations. It takes into account the electron-electron repulsion in a more accurate way, making it a better approximation for multi-electron systems like Helium.

What is a trial wavefunction in the context of the variational method for Helium Atom?

A trial wavefunction is a hypothetical wavefunction that is used in the variational method to approximate the ground state energy of the Helium atom. It is a mathematical function that represents the probability of finding an electron at a certain position in space. The goal of the variational method is to optimize the parameters of the trial wavefunction to get the best possible approximation of the ground state energy.

What are the limitations of the variational method for Helium Atom?

One limitation of the variational method for Helium Atom is that it can only provide an approximation of the ground state energy and does not give exact solutions. It also requires a good initial guess for the trial wavefunction, which can be difficult to obtain for more complex systems. Additionally, the variational method can be computationally intensive and may not always converge to the true ground state energy.

What are the applications of the variational method for Helium Atom?

The variational method has many applications in quantum mechanics, including the study of atoms, molecules, and solids. In the context of Helium Atom, the variational method can be used to calculate other properties such as the electron density and energy levels. It is also used in other fields such as materials science and chemistry to model and understand the behavior of systems with multiple interacting particles.

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