Is Total Angular Momentum Conserved in the Hydrogen Ion Molecule H₂⁺?

In summary, Wolfgang Demtroder claims in his book "Molecular Physics" that for the hydrogen ion molecule ##H_2 ^+##, the total angular momentum in absolute value is a constant quantum number. This is based on Noether's theorem and the fact that the nuclear potential in this molecule is axially symmetric. However, the validity of this claim is questioned by the fact that it is not mentioned in any other book and there is no proof provided by Demtroder.
  • #1
Jamister
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in the book Molecular Physics of Wolfgang Demtroder, he claims for hydrogen ion molecule ##H_2 ^+## the total angular momentum in absolute value is a constant quantum number. I never saw it any other book and I think it's wrong, because there is no reason for it and he doesn't prove it. here is what he says in the book:
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what do you think?
 
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  • #2
This all comes from Noether’s theorem. The nuclear potential in ##H_2^+## is not spherically symmetric, so the total angular momentum is not conserved. However, it is axially symmetric, so quantities associated with the axis of symmetry are conserved.
 
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1. What is a hydrogen ion molecule?

A hydrogen ion molecule is a type of molecule that consists of two hydrogen atoms that are bonded together by a covalent bond. It has a chemical formula of H2 and is the simplest and most abundant molecule in the universe.

2. How is a hydrogen ion molecule formed?

A hydrogen ion molecule is typically formed through a chemical reaction between two hydrogen atoms. This can occur through a process called hydrogenation, where two hydrogen atoms combine in the presence of a catalyst, or through the ionization of a hydrogen atom, which results in the formation of a hydrogen ion molecule.

3. What are the properties of a hydrogen ion molecule?

A hydrogen ion molecule is a colorless, odorless, and highly flammable gas. It is the lightest and most abundant element in the universe and has a boiling point of -252.87°C and a melting point of -259.14°C. It is also highly reactive and can form compounds with other elements.

4. What are the uses of a hydrogen ion molecule?

Hydrogen ion molecules have a wide range of uses in various industries. They are commonly used as a fuel source for rockets and other spacecraft, as well as in the production of ammonia for fertilizers and the manufacture of certain chemicals. They are also being explored as a potential clean energy source for vehicles and power generation.

5. Is a hydrogen ion molecule dangerous?

While hydrogen ion molecules are highly flammable and can pose a risk if not handled properly, they are not inherently dangerous. In fact, they are naturally occurring and essential for many biological processes. However, caution should always be taken when handling and storing hydrogen ion molecules due to their flammability.

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