# Puzzles about the ''groud state manifold''

• wdlang
In summary: So there are two ground states, one with the electron in the nucleus and one with the electron outside the nucleus. But, the ground state with the electron inside the nucleus is usually more stable because it has a higher energy.
wdlang
in atomic physics, sometimes one would encounter the termilogy ''ground state manifold''

my question is, the ground state of an atom is usually unique

How come the ''ground state manifold''?

It means several nearly degenerate level?

are these level stable?

wdlang said:
in atomic physics, sometimes one would encounter the termilogy ''ground state manifold''

my question is, the ground state of an atom is usually unique

How come the ''ground state manifold''?

It means several nearly degenerate level?

are these level stable?

I think you are referring to the spontaneous breakdown of symmetry, right ?

Let's take the example of a ferromagnet. This magnet can be composed out of a gazzillion of iron atoms. Each iron atom will interact with its nearest neighbors by aligning its spin along the direction of the neighbor. This lowers their interaction energy. The lowest possible energy wil be reached once all spins have the same direction. Now, different ground state manifolds means that the system can have different physical ststaes that correspond to the lowest energy state. In our example, the lowest energy corresponds to that system which has all its spins aligned into one direction. But, this direction can be up, down, left, right, in between left and right, etc etc. So there are many possible directions ! Again, what matters is that all spins are aligned ! But the direction of those spins can vary from one system to another. This makes that there are many ground states possible !

marlon

no, it has nothing to do with symmetry spontaneous breaking

the manifold usually consists of just finite levels

they may all belong to the l=2 subspace, so the dimension is just 5.

thanks for your interests anyway.

wdlang said:
no, it has nothing to do with symmetry spontaneous breaking

the manifold usually consists of just finite levels

they may all belong to the l=2 subspace, so the dimension is just 5.

thanks for your interests anyway.

But then what are you asking about ? Ground state manifold just means ground state energy level, that's it.

marlon

hehe, i watched the movies of you on youtube

you are a handsome guy!

wdlang said:
in atomic physics, sometimes one would encounter the termilogy ''ground state manifold''

my question is, the ground state of an atom is usually unique

well... for example, the ground state of a H-atom is doubly degenerate due to electron spin.

## 1. What is the "ground state manifold"?

The "ground state manifold" refers to the set of all possible states of a physical system that have the lowest possible energy. This includes the lowest energy state as well as any degenerate states with the same energy level.

## 2. How is the ground state manifold related to puzzles?

Puzzles about the ground state manifold often involve finding the lowest energy state of a system or understanding the possible states and their energies within the manifold. These puzzles can also be used to study and understand complex physical systems.

## 3. What types of systems have a ground state manifold?

All physical systems have a ground state manifold. It is a fundamental concept in quantum mechanics and can be applied to a wide range of systems, including atoms, molecules, and solids.

## 4. How is the ground state of a system determined?

The ground state of a system is determined by solving the Schrödinger equation, which describes the wave function of a quantum system. This equation takes into account the potential energy and interactions between particles in the system to determine the lowest energy state.

## 5. What are some real-world applications of puzzles about the ground state manifold?

Puzzles about the ground state manifold have practical applications in fields such as materials science, chemistry, and physics. They can be used to understand and design new materials, study the behavior of atoms and molecules, and develop new technologies such as quantum computing.

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